M. F. Atiyah, R. Bott, and A. Shapiro :
“Clifford modules Topology
3 : Supplement 1
(July 1964 ),
pp. 3–38 .
MR
0167985 Zbl
0146.19001 article
People
BibTeX
@article {key0167985m,
AUTHOR = {Atiyah, M. F. and Bott, R. and Shapiro,
A.},
TITLE = {Clifford modules},
JOURNAL = {Topology},
FJOURNAL = {Topology},
VOLUME = {3},
NUMBER = {Supplement 1},
MONTH = {July},
YEAR = {1964},
PAGES = {3--38},
DOI = {10.1016/0040-9383(64)90003-5},
NOTE = {MR:0167985. Zbl:0146.19001.},
ISSN = {0040-9383},
}
M. F. Atiyah and R. Bott :
“The index problem for manifolds with boundary ,”
pp. 175–186
in
Differential Analysis: Papers presented at the international colloquium
(Bombay, 7–14 January 1964 ).
Tata Institute of Fundamental Research Studies in Mathematics 2 .
Oxford University Press (London ),
1964 .
MR
0185606 Zbl
0163.34603 incollection
Abstract
People
BibTeX
The aim of these lectures is to report on the progress of the index problem in the last year. We will describe an extension of the index formula for closed manifolds (see [Atiyah and Singer 1963]) to manifolds with boundary. The work of Section 4, i.e., the proof of the general index theorem from Theorem 1 was done in collaboration with Singer.
@incollection {key0185606m,
AUTHOR = {Atiyah, M. F. and Bott, R.},
TITLE = {The index problem for manifolds with
boundary},
BOOKTITLE = {Differential Analysis: {P}apers presented
at the international colloquium},
SERIES = {Tata Institute of Fundamental Research
Studies in Mathematics},
NUMBER = {2},
PUBLISHER = {Oxford University Press},
ADDRESS = {London},
YEAR = {1964},
PAGES = {175--186},
NOTE = {(Bombay, 7--14 January 1964). MR:0185606.
Zbl:0163.34603.},
ISSN = {0496-9480},
}
M. Atiyah and R. Bott :
“On the periodicity theorem for complex vector bundles Acta Math.
112 : 1
(1964 ),
pp. 229–247 .
MR
0178470 Zbl
0131.38201 article
Abstract
People
BibTeX
The periodicity theorem for the infinite unitary group [Bott 1959] can be interpreted as a statement about complex vector bundles. As such it describes the relation between vector bundles over \( X \) and \( X\times S^2 \) , where \( X \) is a compact space and \( S^2 \) is the 2-sphere. This relation is most succinctly expressed by the formula
\[ K(X\times S^2) \simeq K(X)\otimes K(S^2), \]
where \( K(X) \) is the Grothendieck group of complex vector bundles over \( X \) . The general theory of these \( K \) -groups, as developed in [Atiyah and Hirzebruch 1961], has found many applications in topology and related fields. Since the periodicity theorem is the foundation stone of all this theory it seems desirable to have an elementary proof of it, and it is the purpose of this paper to present such a proof.
@article {key0178470m,
AUTHOR = {Atiyah, Michael and Bott, Raoul},
TITLE = {On the periodicity theorem for complex
vector bundles},
JOURNAL = {Acta Math.},
FJOURNAL = {Acta Mathematica},
VOLUME = {112},
NUMBER = {1},
YEAR = {1964},
PAGES = {229--247},
DOI = {10.1007/BF02391772},
NOTE = {MR:0178470. Zbl:0131.38201.},
ISSN = {0001-5962},
}
M. F. Atiyah and R. Bott :
Notes on the Lefschetz fixed point theorem for elliptic complexes .
Harvard University (Cambridge, MA ),
1964 .
Zbl
0161.43101 book
People
BibTeX
@book {key0161.43101z,
AUTHOR = {Atiyah, Michael F. and Bott, Raoul},
TITLE = {Notes on the {L}efschetz fixed point
theorem for elliptic complexes},
PUBLISHER = {Harvard University},
ADDRESS = {Cambridge, MA},
YEAR = {1964},
PAGES = {92},
NOTE = {Zbl:0161.43101.},
}
M. F. Atiyah and R. Bott :
“A Lefschetz fixed point formula for elliptic differential operators Bull. Am. Math. Soc.
72 : 2
(1966 ),
pp. 245–250 .
MR
0190950 Zbl
0151.31801 article
Abstract
People
BibTeX
The classical Lefschetz fixed point formula expresses, under suitable circumstances, the number of fixed points of a continuous map \( f:X\to X \) in terms of the transformation induced by \( f \) on the cohomology of \( X \) . If \( X \) is not just a topological space but has some further structure, and if this structure is preserved by \( f \) , one would expect to be able to refine the Lefschetz formula and to say more about the nature of the fixed points. The purpose of this note is to present such a refinement (Theorem 1) when \( X \) is a compact differentiable manifold endowed with an elliptic differential operator (or more generally an elliptic complex). Taking essentially the classical operators of complex and Riemannian geometry we obtain a number of important special cases (Theorem 2, 3). The first of these was conjectured to us by Shimura and was proved by Eichler for dimension one.
@article {key0190950m,
AUTHOR = {Atiyah, M. F. and Bott, R.},
TITLE = {A {L}efschetz fixed point formula for
elliptic differential operators},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {72},
NUMBER = {2},
YEAR = {1966},
PAGES = {245--250},
DOI = {10.1090/S0002-9904-1966-11483-0},
NOTE = {MR:0190950. Zbl:0151.31801.},
ISSN = {0002-9904},
}
M. F. Atiyah and R. Bott :
“A Lefschetz fixed point formula for elliptic complexes, I Ann. Math. (2)
86 : 2
(1967 ),
pp. 374–407 .
MR
0212836 Zbl
0161.43201 article
Abstract
People
BibTeX
@article {key0212836m,
AUTHOR = {Atiyah, M. F. and Bott, R.},
TITLE = {A {L}efschetz fixed point formula for
elliptic complexes, {I}},
JOURNAL = {Ann. Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {86},
NUMBER = {2},
YEAR = {1967},
PAGES = {374--407},
DOI = {10.2307/1970694},
NOTE = {MR:0212836. Zbl:0161.43201.},
ISSN = {0003-486X},
}
M. F. Atiyah and R. Bott :
“A Lefschetz fixed point formula for elliptic complexes, II: Applications Ann. Math. (2)
88 : 3
(November 1968 ),
pp. 451–491 .
MR
0232406 Zbl
0167.21703 article
Abstract
People
BibTeX
@article {key0232406m,
AUTHOR = {Atiyah, M. F. and Bott, R.},
TITLE = {A {L}efschetz fixed point formula for
elliptic complexes, {II}: {A}pplications},
JOURNAL = {Ann. Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {88},
NUMBER = {3},
MONTH = {November},
YEAR = {1968},
PAGES = {451--491},
DOI = {10.2307/1970721},
NOTE = {MR:0232406. Zbl:0167.21703.},
ISSN = {0003-486X},
}
M. F. Atiyah, R. Bott, and L. Gårding :
“Lacunas for hyperbolic differential operators with constant coefficients, I Acta Math.
124 : 1
(July 1970 ),
pp. 109–189 .
A Russian translation was published in Usp. Mat. Nauk 26 :2(158)
MR
0470499 Zbl
0191.11203 article
Abstract
People
BibTeX
The theory of lacunas for hyperbolic differential operators was created by I. G. Petrovsky who published the basic paper of the subject in 1945. Although its results are very clear, the paper is difficult reading and has so far not lead to studies of the same scope. We shall clarify and generalize Petrovsky’s theory.
@article {key0470499m,
AUTHOR = {Atiyah, M. F. and Bott, R. and G\aa
rding, L.},
TITLE = {Lacunas for hyperbolic differential
operators with constant coefficients,
{I}},
JOURNAL = {Acta Math.},
FJOURNAL = {Acta Mathematica},
VOLUME = {124},
NUMBER = {1},
MONTH = {July},
YEAR = {1970},
PAGES = {109--189},
DOI = {10.1007/BF02394570},
NOTE = {A Russian translation was published
in \textit{Usp. Mat. Nauk} \textbf{26}:2(158).
MR:0470499. Zbl:0191.11203.},
ISSN = {0001-5962},
}
M. F. At’ja, R. Bott, and L. Gording :
“Lacunas for hyperbolic differential operators with constant coefficients, I Usp. Mat. Nauk
26 : 2(158)
(1971 ),
pp. 25–100 .
Russian translation of an article in Acta Math. 124 :1 (1970)
MR
0606062 Zbl
0208.13201 article
People
BibTeX
@article {key0606062m,
AUTHOR = {At{\cprime}ja, M. F. and Bott, R. and
Gording, L.},
TITLE = {Lacunas for hyperbolic differential
operators with constant coefficients,
{I}},
JOURNAL = {Usp. Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk},
VOLUME = {26},
NUMBER = {2(158)},
YEAR = {1971},
PAGES = {25--100},
URL = {http://mi.mathnet.ru/eng/umn5186},
NOTE = {Russian translation of an article in
\textit{Acta Math.} \textbf{124}:1 (1970).
MR:0606062. Zbl:0208.13201.},
ISSN = {0042-1316},
}
M. Atiyah, R. Bott, and V. K. Patodi :
“On the heat equation and the index theorem ,”
Matematika, Moskva
17 : 6
(1973 ),
pp. 3–48 .
Russian translation of an article in Invent. Math. 19 :4 (1973)
Zbl
0364.58016 article
People
BibTeX
@article {key0364.58016z,
AUTHOR = {Atiyah, Michael and Bott, Raoul and
Patodi, V. K.},
TITLE = {On the heat equation and the index theorem},
JOURNAL = {Matematika, Moskva},
VOLUME = {17},
NUMBER = {6},
YEAR = {1973},
PAGES = {3--48},
NOTE = {Russian translation of an article in
\textit{Invent. Math.} \textbf{19}:4
(1973). Zbl:0364.58016.},
}
M. Atiyah, R. Bott, and V. K. Patodi :
“On the heat equation and the index theorem Invent. Math.
19 : 4
(1973 ),
pp. 279–330 .
Dedicated to Sir William Hodge on his 70th birthday.
Errata were published in Invent. Math. 28 :3 (1975)Matematika 17 :6 (1973)
MR
0650828 Zbl
0257.58008 article
Abstract
People
BibTeX
@article {key0650828m,
AUTHOR = {Atiyah, M. and Bott, R. and Patodi,
V. K.},
TITLE = {On the heat equation and the index theorem},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {19},
NUMBER = {4},
YEAR = {1973},
PAGES = {279--330},
DOI = {10.1007/BF01425417},
NOTE = {Dedicated to Sir William Hodge on his
70th birthday. Errata were published
in \textit{Invent. Math.} \textbf{28}:3
(1975). A Russian translation was published
in \textit{Matematika} \textbf{17}:6
(1973). MR:0650828. Zbl:0257.58008.},
ISSN = {0020-9910},
}
M. F. Atiyah, R. Bott, and L. Gårding :
“Lacunas for hyperbolic differential operators with constant coefficients, II Acta Math.
131 : 1
(December 1973 ),
pp. 145–206 .
A Russian translation was published in Usp. Mat. Nauk 39 :3(237)
MR
0470500 Zbl
0266.35045 article
People
BibTeX
@article {key0470500m,
AUTHOR = {Atiyah, M. F. and Bott, R. and G\aa
rding, L.},
TITLE = {Lacunas for hyperbolic differential
operators with constant coefficients,
{II}},
JOURNAL = {Acta Math.},
FJOURNAL = {Acta Mathematica},
VOLUME = {131},
NUMBER = {1},
MONTH = {December},
YEAR = {1973},
PAGES = {145--206},
DOI = {10.1007/BF02392039},
NOTE = {A Russian translation was published
in \textit{Usp. Mat. Nauk} \textbf{39}:3(237).
MR:0470500. Zbl:0266.35045.},
ISSN = {0001-5962},
}
M. Atiyah, R. Bott, and V. K. Patodi :
“Errata to: ‘On the heat equation and the index theorem’ Invent. Math.
28 : 3
(1975 ),
pp. 277–280 .
Errata for article in Invent. Math. 19 :4 (1973)
MR
0650829 Zbl
0301.58018 article
Abstract
People
BibTeX
The joint paper of the above title which appeared in Inventiones Math. 19 , 279–330 (1973), though correct in principle, contained some technical errors which we shall here explain and rectify. Our thanks are due to D. Epstein, Y. Colin de Verdiére and A. Vasquez whose computations and queries alerted us to our errors.
@article {key0650829m,
AUTHOR = {Atiyah, M. and Bott, R. and Patodi,
V. K.},
TITLE = {Errata to: ``{O}n the heat equation
and the index theorem''},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {28},
NUMBER = {3},
YEAR = {1975},
PAGES = {277--280},
DOI = {10.1007/BF01425562},
NOTE = {Errata for article in \textit{Invent.
Math.} \textbf{19}:4 (1973). MR:0650829.
Zbl:0301.58018.},
ISSN = {0020-9910},
}
M. F. Atiyah and R. Bott :
“Yang–Mills and bundles over algebraic curves ,”
pp. 11–20
in
Geometry and analysis: Papers dedicated to the memory of V. K. Patodi .
Indian Academy of Sciences (Bangalore ),
1980 .
Republished in Proc. Indian Acad. Sci. Math. Sci. 90 :1 (1981)
MR
592249 Zbl
0482.14007 incollection
People
BibTeX
@incollection {key592249m,
AUTHOR = {Atiyah, M. F. and Bott, R.},
TITLE = {Yang--{M}ills and bundles over algebraic
curves},
BOOKTITLE = {Geometry and analysis: {P}apers dedicated
to the memory of {V}.~{K}. {P}atodi},
PUBLISHER = {Indian Academy of Sciences},
ADDRESS = {Bangalore},
YEAR = {1980},
PAGES = {11--20},
NOTE = {Republished in \textit{Proc. Indian
Acad. Sci. Math. Sci.} \textbf{90}:1
(1981). MR:592249. Zbl:0482.14007.},
ISBN = {9780387102702},
}
M. F. Atiyah and R. Bott :
“Yang–Mills and bundles over algebraic curves 11–20
in
Geometry and analysis: Papers dedicated to the memory of V. K. Patodi ,
published as Proc. Indian Acad. Sci., Math. Sci.
90 : 1 .
Indian Academy of Sciences (Bangalore ),
1981 .
MR
653942 Zbl
0499.14005 incollection
People
BibTeX
@article {key653942m,
AUTHOR = {Atiyah, M. F. and Bott, R.},
TITLE = {Yang--{M}ills and bundles over algebraic
curves},
JOURNAL = {Proc. Indian Acad. Sci., Math. Sci.},
FJOURNAL = {Proceedings of the Indian Academy of
Sciences. Mathematical Sciences},
VOLUME = {90},
NUMBER = {1},
YEAR = {1981},
PAGES = {11--20},
DOI = {10.1007/BF02867013},
NOTE = {\textit{Geometry and analysis: {P}apers
dedicated to the memory of {V}.~{K}.
{P}atodi}. MR:653942. Zbl:0499.14005.},
ISSN = {0253-4142},
ISBN = {9780387102702},
}
M. F. Atiyah and R. Bott :
“The Yang–Mills equations over Riemann surfaces Philos. Trans. R. Soc. Lond., A
308 : 1505
(1983 ),
pp. 523–615 .
MR
702806 Zbl
0509.14014 article
Abstract
People
BibTeX
The Yang–Mills functional over a Riemann surface is studied from the point of view of Morse theory. The main result is that this is a ‘perfect’ functional provided due account is taken of its gauge symmetry. This enables topological conclusions to be drawn about the critical sets and leads eventually to information about the moduli space of algebraic bundles over the Riemann surface. This in turn depends on the interplay between the holomorphic and unitary structures, which is analysed in detail.
@article {key702806m,
AUTHOR = {Atiyah, M. F. and Bott, R.},
TITLE = {The {Y}ang--{M}ills equations over {R}iemann
surfaces},
JOURNAL = {Philos. Trans. R. Soc. Lond., A},
FJOURNAL = {Philosophical Transactions of the Royal
Society of London. Series A. Mathematical
and Physical Sciences},
VOLUME = {308},
NUMBER = {1505},
YEAR = {1983},
PAGES = {523--615},
DOI = {10.1098/rsta.1983.0017},
NOTE = {MR:702806. Zbl:0509.14014.},
ISSN = {0080-4614},
CODEN = {PTRMAD},
}
M. F. Atiyah and R. Bott :
“The moment map and equivariant cohomology Topology
23 : 1
(1984 ),
pp. 1–28 .
MR
721448 Zbl
0521.58025 article
Abstract
People
BibTeX
The purpose of this note is to present a de Rham version of the localization theorems of equivariant cohomology, and to point out their relation to a recent result of Duistermaat and Heckman and also to a quite independent result of Witten. To a large extent all the material that we use has been around for some time, although equivariant cohomology is not perhaps familiar to analysts. Our contribution is therefore mainly an expository one linking together various points of view.
@article {key721448m,
AUTHOR = {Atiyah, M. F. and Bott, R.},
TITLE = {The moment map and equivariant cohomology},
JOURNAL = {Topology},
FJOURNAL = {Topology},
VOLUME = {23},
NUMBER = {1},
YEAR = {1984},
PAGES = {1--28},
DOI = {10.1016/0040-9383(84)90021-1},
NOTE = {MR:721448. Zbl:0521.58025.},
ISSN = {0040-9383},
CODEN = {TPLGAF},
}
M. F. At’ya, R. Bott, and L. Gårding :
“Lacunas for hyperbolic differential operators with constant coefficients, II Usp. Mat. Nauk
39 : 3(237)
(1984 ),
pp. 171–224 .
Russian translation of an article in Acta Math. 131 :1 (1973)
MR
747794 Zbl
0568.35058 article
People
BibTeX
@article {key747794m,
AUTHOR = {At{\cprime}ya, M. F. and Bott, R. and
G\aa rding, L.},
TITLE = {Lacunas for hyperbolic differential
operators with constant coefficients,
{II}},
JOURNAL = {Usp. Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk},
VOLUME = {39},
NUMBER = {3(237)},
YEAR = {1984},
PAGES = {171--224},
URL = {http://mi.mathnet.ru/eng/umn2374},
NOTE = {Russian translation of an article in
\textit{Acta Math.} \textbf{131}:1 (1973).
MR:747794. Zbl:0568.35058.},
ISSN = {0042-1316},
}
M. Atiyah :
“Contribution to the collected works of Raoul Bott ,”
pp. xxix–xxx
in
Raoul Bott: Collected papers ,
vol. 2: Differential operators .
Edited by R. D. MacPherson .
Contemporary Mathematicians .
Birkhäuser (Boston ),
1994 .
MR
1290365 incollection
People
BibTeX
@incollection {key1290365m,
AUTHOR = {Atiyah, M.},
TITLE = {Contribution to the collected works
of {R}aoul {B}ott},
BOOKTITLE = {Raoul {B}ott: {C}ollected papers},
EDITOR = {MacPherson, R. D.},
VOLUME = {2: Differential operators},
SERIES = {Contemporary Mathematicians},
PUBLISHER = {Birkh\"auser},
ADDRESS = {Boston},
YEAR = {1994},
PAGES = {xxix--xxx},
NOTE = {MR:1290365.},
ISSN = {0884-7037},
ISBN = {9780817636463},
}
V. Vassiliev :
“The mathematical legacy of ‘Lacunas for hyperbolic differential equations’ ,”
pp. xxiii–xxviii
in
Raoul Bott: Collected papers ,
vol. 2: Differential operators .
Edited by R. D. MacPherson .
Contemporary Mathematicians .
Birkhäuser (Boston, MA ),
1994 .
Commentary on two-part article published in Acta Math. 124 (1970)Acta Math. 131 (1973)
MR
1290364 incollection
People
BibTeX
@incollection {key1290364m,
AUTHOR = {Vassiliev, Victor},
TITLE = {The mathematical legacy of ``{L}acunas
for hyperbolic differential equations''},
BOOKTITLE = {Raoul {B}ott: {C}ollected papers},
EDITOR = {Robert D. MacPherson},
VOLUME = {2: Differential operators},
SERIES = {Contemporary Mathematicians},
PUBLISHER = {Birkh\"auser},
ADDRESS = {Boston, MA},
YEAR = {1994},
PAGES = {xxiii--xxviii},
NOTE = {Commentary on two-part article published
in \textit{Acta Math.} \textbf{124}
(1970) and \textit{Acta Math.} \textbf{131}
(1973). MR:1290364.},
ISSN = {0884-7037},
ISBN = {9780817636463},
}
M. Atiyah :
“Reflections on geometry and physics ,”
pp. 423–428
in
Geometry, topology, & physics: Lectures of a conference in honor of Raoul Bott’s 70th birthday
(Harvard University, April 1993 ).
Edited by S.-T. Yau .
Conference proceedings and lecture notes in geometry and topology 4 .
International Press (Cambridge, MA ),
1995 .
MR
1358626 incollection
People
BibTeX
@incollection {key1358626m,
AUTHOR = {Atiyah, Michael},
TITLE = {Reflections on geometry and physics},
BOOKTITLE = {Geometry, topology, \& physics: {L}ectures
of a conference in honor of {R}aoul
{B}ott's 70th birthday},
EDITOR = {Shing-Tung Yau},
SERIES = {Conference proceedings and lecture notes
in geometry and topology},
NUMBER = {4},
PUBLISHER = {International Press},
ADDRESS = {Cambridge, MA},
YEAR = {1995},
PAGES = {423--428},
NOTE = {(Harvard University, April 1993). MR:1358626.},
ISBN = {9781571460240},
}
L. Gårding :
“A happy collaboration ,”
pp. xlix–liv
in
Sir Michael Atiyah: A great mathematician of the twentieth century ,
published as Asian J. Math.
3 : 1
(1999 ).
Dedicated to Michael Atiyah and Raoul Bott.
MR
1701917 Zbl
0955.01017 incollection
People
BibTeX
@article {key1701917m,
AUTHOR = {G{\aa}rding, Lars},
TITLE = {A happy collaboration},
JOURNAL = {Asian J. Math.},
FJOURNAL = {Asian Journal of Mathematics},
VOLUME = {3},
NUMBER = {1},
YEAR = {1999},
PAGES = {xlix--liv},
NOTE = {\textit{Sir {M}ichael {A}tiyah: {A}
great mathematician of the twentieth
century}. Dedicated to Michael Atiyah
and Raoul Bott. MR:1701917. Zbl:0955.01017.},
ISSN = {1093-6106},
ISBN = {9781571460806},
}
Papers dedicated to Atiyah, Bott, Hirzebruch, and Singer .
Edited by S.-T. Yau .
Surveys in Differential Geometry (supplement to Journal of Differential Geometry) 7 .
International Press (Somerville, MA ),
2000 .
MR
1919419 book
People
BibTeX
@book {key1919419m,
TITLE = {Papers dedicated to {A}tiyah, {B}ott,
{H}irzebruch, and {S}inger},
EDITOR = {Shing-Tung Yau},
SERIES = {Surveys in Differential Geometry (supplement
to {J}ournal of {D}ifferential {G}eometry)},
NUMBER = {7},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2000},
PAGES = {696},
NOTE = {MR:1919419.},
ISSN = {1052-9233},
ISBN = {9781571461780},
}
E. Witten :
“Michael Atiyah and the physics/geometry interface ,”
pp. 43–50
in
The founders of index theory: Reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Singer .
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2003 .
Republished from Asian J. Math. 3 :1 (1999)2009 edition of the book.
incollection
People
BibTeX
@incollection {key91870136,
AUTHOR = {Witten, Edward},
TITLE = {Michael {A}tiyah and the physics/geometry
interface},
BOOKTITLE = {The founders of index theory: {R}eminiscences
of and about {S}ir {M}ichael {A}tiyah,
{R}aoul {B}ott, {F}riedrich {H}irzebruch,
and {I}.~{M}. {S}inger},
EDITOR = {Yau, Shing-Tung},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2003},
PAGES = {43--50},
NOTE = {Republished from \textit{Asian J. Math.}
\textbf{3}:1 (1999). Also in the 2009
edition of the book.},
ISBN = {9781571461209},
}
N. Hitchin :
“Sir Michael Atiyah: A brief biography ,”
pp. 15–22
in
The founders of index theory: Reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Singer .
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2003 .
Also in the 2009 edition of the book.
incollection
People
BibTeX
@incollection {key29362485,
AUTHOR = {Hitchin, Nigel},
TITLE = {Sir {M}ichael {A}tiyah: {A} brief biography},
BOOKTITLE = {The founders of index theory: {R}eminiscences
of and about {S}ir {M}ichael {A}tiyah,
{R}aoul {B}ott, {F}riedrich {H}irzebruch,
and {I}.~{M}. {S}inger},
EDITOR = {Yau, Shing-Tung},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2003},
PAGES = {15--22},
NOTE = {Also in the 2009 edition of the book.},
ISBN = {9781571461209},
}
M. Atiyah :
“The conscience of science ,”
pp. 51–66
in
The founders of index theory: Reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Singer .
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2003 .
Also in the 2009 edition of the book.
incollection
People
BibTeX
@incollection {key73905347,
AUTHOR = {Atiyah, Michael},
TITLE = {The conscience of science},
BOOKTITLE = {The founders of index theory: {R}eminiscences
of and about {S}ir {M}ichael {A}tiyah,
{R}aoul {B}ott, {F}riedrich {H}irzebruch,
and {I}.~{M}. {S}inger},
EDITOR = {Yau, Shing-Tung},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2003},
PAGES = {51--66},
NOTE = {Also in the 2009 edition of the book.},
ISBN = {9781571461209},
}
G. Lusztig :
“Recollections about my teacher Michael Atiyah ,”
pp. 37–42
in
The founders of index theory: Reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Singer .
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2003 .
Republished from Asian J. Math. 3 :1 (1999)2009 edition of the book.
incollection
People
BibTeX
@incollection {key99039880,
AUTHOR = {Lusztig, George},
TITLE = {Recollections about my teacher {M}ichael
{A}tiyah},
BOOKTITLE = {The founders of index theory: {R}eminiscences
of and about {S}ir {M}ichael {A}tiyah,
{R}aoul {B}ott, {F}riedrich {H}irzebruch,
and {I}.~{M}. {S}inger},
EDITOR = {Yau, Shing-Tung},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2003},
PAGES = {37--42},
NOTE = {Republished from \textit{Asian J. Math.}
\textbf{3}:1 (1999). Also in the 2009
edition of the book.},
ISBN = {9781571461209},
}
P. Goddard :
“Sir Michael Atiyah and the early days of the Newton Institute ,”
pp. 23–28
in
The founders of index theory: Reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Singer .
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2003 .
Also in the 2009 edition of the book.
incollection
People
BibTeX
@incollection {key56102705,
AUTHOR = {Goddard, P.},
TITLE = {Sir {M}ichael {A}tiyah and the early
days of the {N}ewton {I}nstitute},
BOOKTITLE = {The founders of index theory: {R}eminiscences
of and about {S}ir {M}ichael {A}tiyah,
{R}aoul {B}ott, {F}riedrich {H}irzebruch,
and {I}.~{M}. {S}inger},
EDITOR = {Yau, Shing-Tung},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2003},
PAGES = {23--28},
NOTE = {Also in the 2009 edition of the book.},
ISBN = {9781571461209},
}
The founders of index theory: Reminiscences of Atiyah, Bott, Hirzebruch, and Singer .
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2003 .
Republished in 2009 .
MR
2136846 Zbl
1072.01021 book
People
BibTeX
@book {key2136846m,
TITLE = {The founders of index theory: {R}eminiscences
of {A}tiyah, {B}ott, {H}irzebruch, and
{S}inger},
EDITOR = {Yau, S.-T.},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2003},
PAGES = {liv+358},
NOTE = {Republished in 2009. MR:2136846. Zbl:1072.01021.},
ISBN = {9781571461209},
}
M. Atiyah :
“Raoul Harry Bott: 24 September 1923–20 December 2005 Biogr. Mems Fell. R. Soc.
53
(December 2007 ),
pp. 63–76 .
Republished in Bull. Lond. Math. Soc. 42 :1 (2010)
article
Abstract
People
BibTeX
Read it here
@article {key36746141,
AUTHOR = {Atiyah, Michael},
TITLE = {Raoul {H}arry {B}ott: 24 {S}eptember
1923--20 {D}ecember 2005},
JOURNAL = {Biogr. Mems Fell. R. Soc.},
FJOURNAL = {Biographical Memoirs of Fellows of the
Royal Society},
VOLUME = {53},
MONTH = {December},
YEAR = {2007},
PAGES = {63--76},
DOI = {10.1098/rsbm.2007.0006},
NOTE = {Republished in \textit{Bull. Lond. Math.
Soc.} \textbf{42}:1 (2010).},
ISSN = {0080-4606},
}
M. F. Atiyah :
“A personal history ,”
pp. 5–15
in
The founders of index theory: Reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Singer ,
2nd edition.
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2009 .
Republished in Atiyah’s Collected works , vol. 6 .
incollection
People
BibTeX
@incollection {key72270854,
AUTHOR = {Atiyah, M. F.},
TITLE = {A personal history},
BOOKTITLE = {The founders of index theory: {R}eminiscences
of and about {S}ir {M}ichael {A}tiyah,
{R}aoul {B}ott, {F}riedrich {H}irzebruch,
and {I}.~{M}. {S}inger},
EDITOR = {Yau, Shing-Tung},
EDITION = {2nd},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2009},
PAGES = {5--15},
NOTE = {Republished in Atiyah's \textit{Collected
works}, vol.~6.},
ISBN = {9781571461377},
}
S. Donaldson :
“Geometry in Oxford c.1980–85 ,”
pp. 35–42
in
The founders of index theory: Reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Singer ,
2nd edition.
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2009 .
Republished from Asian J. Math. 3 :1 (1999)2003 edition of the book.
incollection
Abstract
People
BibTeX
The first part of this essay comprises some brief reminiscences from my time as a research student of Sir Michael Atiyah: these will be commonplace to my contemporaries, but perhaps younger mathematicians may be less familiar with the research interests of this period. In the second part of the essay I will discuss some current research questions.
@incollection {key12598427,
AUTHOR = {Donaldson, Simon},
TITLE = {Geometry in {O}xford c.1980--85},
BOOKTITLE = {The founders of index theory: {R}eminiscences
of and about {S}ir {M}ichael {A}tiyah,
{R}aoul {B}ott, {F}riedrich {H}irzebruch,
and {I}.~{M}. {S}inger},
EDITOR = {Yau, Shing-Tung},
EDITION = {2nd},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2009},
PAGES = {35--42},
NOTE = {Republished from \textit{Asian J. Math.}
\textbf{3}:1 (1999). Also in the 2003
edition of the book.},
ISBN = {9781571461377},
}
L. Nirenberg :
“Memories of Michael Atiyah ,”
pp. 45–46
in
The founders of index theory: Reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Singer ,
2nd edition.
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2009 .
incollection
People
BibTeX
@incollection {key31967768,
AUTHOR = {Nirenberg, Louis},
TITLE = {Memories of {M}ichael {A}tiyah},
BOOKTITLE = {The founders of index theory: {R}eminiscences
of and about {S}ir {M}ichael {A}tiyah,
{R}aoul {B}ott, {F}riedrich {H}irzebruch,
and {I}.~{M}. {S}inger},
EDITOR = {Yau, Shing-Tung},
EDITION = {2nd},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2009},
PAGES = {45--46},
ISBN = {9781571461377},
}
M. Atiyah :
“Memories of Raoul Bott ,”
pp. 89–94
in
The founders of index theory: Reminiscences of Atiyah, Bott, Hirzebruch, and Singer .
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2009 .
incollection
People
BibTeX
@incollection {key53064164,
AUTHOR = {Atiyah, Michael},
TITLE = {Memories of {R}aoul {B}ott},
BOOKTITLE = {The founders of index theory: {R}eminiscences
of {A}tiyah, {B}ott, {H}irzebruch, and
{S}inger},
EDITOR = {Yau, S.-T.},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2009},
PAGES = {89--94},
ISBN = {9781571461377},
}
M. Atiyah :
“Letter to Raoul, Fritz, and Is ,”
pp. 323–324
in
The founders of index theory: Reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Singer ,
2nd edition.
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2009 .
Also found in the 2003 edition of the book.
incollection
People
BibTeX
@incollection {key46159632,
AUTHOR = {Atiyah, Michael},
TITLE = {Letter to {R}aoul, {F}ritz, and {I}s},
BOOKTITLE = {The founders of index theory: {R}eminiscences
of and about {S}ir {M}ichael {A}tiyah,
{R}aoul {B}ott, {F}riedrich {H}irzebruch,
and {I}.~{M}. {S}inger},
EDITOR = {Yau, Shing-Tung},
EDITION = {2nd},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2009},
PAGES = {323--324},
NOTE = {Also found in the 2003 edition of the
book.},
ISBN = {9781571461377},
}
R. Bott :
“A letter from Raoul Bott ,”
pp. 33–34
in
The founders of index theory: Reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Singer ,
2nd edition.
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2009 .
Also in the 2003 edition of the book.
incollection
People
BibTeX
@incollection {key40178879,
AUTHOR = {Bott, Raoul},
TITLE = {A letter from {R}aoul {B}ott},
BOOKTITLE = {The founders of index theory: {R}eminiscences
of and about {S}ir {M}ichael {A}tiyah,
{R}aoul {B}ott, {F}riedrich {H}irzebruch,
and {I}.~{M}. {S}inger},
EDITOR = {Yau, Shing-Tung},
EDITION = {2nd},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2009},
PAGES = {33--34},
NOTE = {Also in the 2003 edition of the book.},
ISBN = {9781571461377},
}
G. Segal :
“Being a graduate student of Michael Atiyah ,”
pp. 47–48
in
The founders of index theory: Reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Singer ,
2nd edition.
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2009 .
Also in the 2003 edition of the book.
incollection
People
BibTeX
@incollection {key94049467,
AUTHOR = {Segal, Graeme},
TITLE = {Being a graduate student of {M}ichael
{A}tiyah},
BOOKTITLE = {The founders of index theory: {R}eminiscences
of and about {S}ir {M}ichael {A}tiyah,
{R}aoul {B}ott, {F}riedrich {H}irzebruch,
and {I}.~{M}. {S}inger},
EDITOR = {Yau, Shing-Tung},
EDITION = {2nd},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2009},
PAGES = {47--48},
NOTE = {Also in the 2003 edition of the book.},
ISBN = {9781571461377},
}
M. Atiyah :
“Mathematics: Queen and servant of the sciences ,”
pp. 55–76
in
The founders of index theory: Reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Singer ,
2nd edition.
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2009 .
Republished from Proc. Am. Phil. Soc. 137 :4 (1993)Asian J. Math. 3 :1 (1999)
incollection
People
BibTeX
@incollection {key74724142,
AUTHOR = {Atiyah, Michael},
TITLE = {Mathematics: {Q}ueen and servant of
the sciences},
BOOKTITLE = {The founders of index theory: {R}eminiscences
of and about {S}ir {M}ichael {A}tiyah,
{R}aoul {B}ott, {F}riedrich {H}irzebruch,
and {I}.~{M}. {S}inger},
EDITOR = {Yau, Shing-Tung},
EDITION = {2nd},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2009},
PAGES = {55--76},
NOTE = {Republished from \textit{Proc. Am. Phil.
Soc.} \textbf{137}:4 (1993). See also
\textit{Asian J. Math.} \textbf{3}:1
(1999).},
ISBN = {9781571461377},
}
The founders of index theory: Reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I. M. Singer ,
2nd edition.
Edited by S.-T. Yau .
International Press (Somerville, MA ),
2009 .
Republication of 2003 original .
MR
2547480 Zbl
1195.01090 book
People
BibTeX
@book {key2547480m,
TITLE = {The founders of index theory: {R}eminiscences
of and about {S}ir {M}ichael {A}tiyah,
{R}aoul {B}ott, {F}riedrich {H}irzebruch,
and {I}.~{M}. Singer},
EDITOR = {Yau, S.-T.},
EDITION = {2nd},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2009},
PAGES = {lii+393},
NOTE = {Republication of 2003 original. MR:2547480.
Zbl:1195.01090.},
ISBN = {9781571461377},
}
M. Atiyah :
“Working with Raoul Bott: From geometry to physics ,”
pp. 51–61
in
A celebration of the mathematical legacy of Raoul Bott
(Montréal, QC, 9–13 June 2008 ).
Edited by P. R. Kotiuga .
CRM Proceedings & Lecture Notes 50 .
American Mathematical Society (Providence, RI ),
2010 .
MR
2648885 Zbl
1195.01022 incollection
People
BibTeX
@incollection {key2648885m,
AUTHOR = {Atiyah, Michael},
TITLE = {Working with {R}aoul {B}ott: {F}rom
geometry to physics},
BOOKTITLE = {A celebration of the mathematical legacy
of {R}aoul {B}ott},
EDITOR = {Kotiuga, P. Robert},
SERIES = {CRM Proceedings \& Lecture Notes},
NUMBER = {50},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {2010},
PAGES = {51--61},
NOTE = {(Montr\'eal, QC, 9--13 June 2008). MR:2648885.
Zbl:1195.01022.},
ISSN = {1065-8580},
ISBN = {9780821847770},
}
M. Atiyah :
“Obituary: Raoul Harry Bott, FRS, 1923–2005 Bull. Lond. Math. Soc.
42 : 1
(2010 ),
pp. 170–180 .
Republication of an article in Biogr. Mems Fell. R. Soc. 53 (2007)
MR
2586977 Zbl
1181.01039 article
Abstract
People
BibTeX
@article {key2586977m,
AUTHOR = {Atiyah, Michael},
TITLE = {Obituary: {R}aoul {H}arry {B}ott, {FRS},
1923--2005},
JOURNAL = {Bull. Lond. Math. Soc.},
FJOURNAL = {Bulletin of the London Mathematical
Society},
VOLUME = {42},
NUMBER = {1},
YEAR = {2010},
PAGES = {170--180},
DOI = {10.1112/blms/bdp083},
NOTE = {Republication of an article in \textit{Biogr.
Mems Fell. R. Soc.} \textbf{53} (2007).
MR:2586977. Zbl:1181.01039.},
ISSN = {0024-6093},
}
