M. F. Atiyah and F. Hirzebruch :
“Riemann–Roch theorems for differentiable manifolds Bull. Am. Math. Soc.
65 : 4
(1959 ),
pp. 276–281 .
MR
110106 Zbl
0142.40901 article
Abstract
People
BibTeX
The Riemann–Roch Theorem for an algebraic variety \( Y \) (see [Hirzebruch 1956]) led to certain divisibility conditions for the Chern classes of \( Y \) . It was natural to ask whether these conditions held more generally for any compact almost complex manifold. This question, and various generalizations of it, were raised in [Hirzebruch 1954] and most of these have since been answered in the affirmative in [Borel and Hirzebruch 1958] and [Milnor 1960].
More recently Grothendieck has obtained [Borel and Serre 1958] a more general Riemann–Roch Theorem for a map \( f: Y\to X \) of algebraic varieties. This reduces to the previous Riemann–Roch Theorem on taking \( X \) to be a point. Grothendieck’s Theorem implies many conditions on characteristic classes, and again it is natural to ask if these conditions hold more generally for almost complex or even differentiable manifolds. The purpose of this note is to enunciate certain differentiable analogues of Grothendieck’s Theorem. These “differentiable Riemann–Roch Theorems” yield, as special cases, the divisibility conditions mentioned above and also certain new homotopy invariance properties of Pontrjagin classes. As an application of the latter we get a new proof (and slight improvement) of the result of Kervaire–Milnor [1960] on the stable \( J \) -homomorphism.
Another differentiable Riemann–Roch Theorem, with applications to embeddability problems of differentiable manifolds, will be found in [Atiyah and Hirzebruch 1959].
The proofs of our theorems rely heavily on the Bott periodicity of the classical groups [Bott 1957, 1958, 1959], and are altogether different from the earlier methods of [Borel and Hirzebruch 1958] and [Milnor 1960], which were based on Thom’s cobordism theory and Adams’ spectral sequence.
@article {key110106m,
AUTHOR = {Atiyah, M. F. and Hirzebruch, F.},
TITLE = {Riemann--{R}och theorems for differentiable
manifolds},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {65},
NUMBER = {4},
YEAR = {1959},
PAGES = {276--281},
DOI = {10.1090/S0002-9904-1959-10344-X},
NOTE = {MR:110106. Zbl:0142.40901.},
ISSN = {0002-9904},
}
M. F. Atiyah and F. Hirzebruch :
“Quelques théorèmes de non-plongement pour les variétés différentiables Some non-immersion theorems for differentiable manifolds ],
Bull. Soc. Math. France
87
(1959 ),
pp. 383–396 .
MR
114231 Zbl
0196.55903 article
Abstract
People
BibTeX
Nous avons montré dans [Atiyah and Hirzebruch 1959] que le théorème de Riemann–Roch [Borel and Serre 1958] a des analogues différentiables. Un exposé de ces résultats a été fait par l’un des auteurs au Séminaire Bourbaki [Hirzebruch 1958/59]. Les théorèmes de Riemann–Roch différentiables fournissent comme cas particulier certaines conditions de divisibilité pour les classes caractéristiques d’une variété différentiable que l’on peut considérer comme des analogues différentiables du théorème de Riemann–Roch de [Hirzebruch 1956].
La plupart de ces conditions de divisibilité ont été prouvées précédement dans [Borel and Hirzebruch 1958], [Borel and Hirzebruch 1960] et [Milnor 1960]. Dans ce qui suit nous démontrons à l’aide des méthodes de [Atiyah and Hirzebruch 1959] que les classes caractéristiques d’une variété différentiable compacte orientée de dimension \( d \) satisfont aux conditions de divisibilité supplémentaires si la variété peut être différentiablement plongée dans un espace euclidien (ou ce qui est équivalent, une sphère) de dimension \( 2d - q \) . Ces conditions de divisibilité «non stables» nous permettent de prouver des théorèmes de non-plongement qui semblent beaucoup plus forts que ceux qui étaient connus avant (3.6). L’outil essentiel est encore le théorème de Bott [Borel and Hirzebruch 1958/59; Bott 1958] qui dit que la \( n \) -ième classe de Chern d’un fibré vectoriel complexe sur la sphère \( S_{2n} \) est divisible par \( (n-1)! \) .
@article {key114231m,
AUTHOR = {Atiyah, Michael F. and Hirzebruch, Friedrich},
TITLE = {Quelques th\'eor\`emes de non-plongement
pour les vari\'et\'es diff\'erentiables
[Some non-immersion theorems for differentiable
manifolds]},
JOURNAL = {Bull. Soc. Math. France},
FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique
de France},
VOLUME = {87},
YEAR = {1959},
PAGES = {383--396},
URL = {http://www.numdam.org/item?id=BSMF_1959__87__383_0},
NOTE = {MR:114231. Zbl:0196.55903.},
ISSN = {0037-9484},
}
M. F. Atiyah and F. Hirzebruch :
“Vector bundles and homogeneous spaces ,”
pp. 7–38
in
Differential geometry
(Tucson, AZ, 18–19 February 1960 ).
Edited by C. B. Allendoerfer .
Proceedings of Symposia in Pure Mathematics 3 .
American Mathematical Society (Providence, RI ),
1961 .
Republished in Algebraic topology: A student’s guide (1972)
MR
139181 Zbl
0108.17705 incollection
People
BibTeX
@incollection {key139181m,
AUTHOR = {Atiyah, M. F. and Hirzebruch, F.},
TITLE = {Vector bundles and homogeneous spaces},
BOOKTITLE = {Differential geometry},
EDITOR = {Allendoerfer, Carl Barnett},
SERIES = {Proceedings of Symposia in Pure Mathematics},
NUMBER = {3},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1961},
PAGES = {7--38},
NOTE = {(Tucson, AZ, 18--19 February 1960).
Republished in \textit{Algebraic topology:
A student's guide} (1972). MR:139181.
Zbl:0108.17705.},
ISSN = {1098-3627},
}
M. F. Atiyah and F. Hirzebruch :
“Cohomologie-Operationen und charakteristische Klassen Cohomology operations and characteristic classes ],
Math. Z.
77 : 1
(1961 ),
pp. 149–187 .
Dedicated to Friedrich Karl Schmidt on the occasion of his sixtieth birthday.
MR
156361 Zbl
0109.16002 article
People
BibTeX
@article {key156361m,
AUTHOR = {Atiyah, M. F. and Hirzebruch, F.},
TITLE = {Cohomologie-{O}perationen und charakteristische
{K}lassen [Cohomology operations and
characteristic classes]},
JOURNAL = {Math. Z.},
FJOURNAL = {Mathematische Zeitschrift},
VOLUME = {77},
NUMBER = {1},
YEAR = {1961},
PAGES = {149--187},
DOI = {10.1007/BF01180171},
NOTE = {Dedicated to Friedrich Karl Schmidt
on the occasion of his sixtieth birthday.
MR:156361. Zbl:0109.16002.},
ISSN = {0025-5874},
}
M. F. Atiyah and F. Hirzebruch :
“Bott periodicity and the parallelizability of the spheres Proc. Camb. Philos. Soc.
57 : 2
(April 1961 ),
pp. 223–226 .
MR
126282 Zbl
0108.35902 article
Abstract
People
BibTeX
The theorems of Bott [1958, 1959a] on the stable homotopy of the classical groups imply that the sphere \( S^n \) is not parallelizable for \( n \neq 1 \) , \( 3, 7 \) . This was shown independently by Kervaire [1958] and Milnor [1958; Bott and Milnor 1958]. Another proof can be found in [Borel and Hirzebruch 1959, §26.11]. The work of J. F. Adams (on the non-existence of elements of Hopf invariant one) implies more strongly that \( S^n \) with any (perhaps extraordinary) differentiable structure is not parallelizable if \( n \neq 1 \) , \( 3, 7 \) . Thus there exist already four proofs for the non-parallelizability of the spheres, the first three mentioned relying on the Bott theory, as given in [Bott 1958, 1959a]. The purpose of this note is to show how the refined form of Bott’s results given in [Bott 1959b] leads to a very simple proof of the non-parallelizability (only for the usual differentiable structures of the spheres). We shall prove in fact the folowing theorem due to Milnor [1958] which implies the non-parallelizability.
There exists a real vector bundle \( \xi \) over the sphere \( S^n \) with \( w_n(\xi) \neq 0 \) only for \( n = 1 \) , \( 2,4 \) or 8
@article {key126282m,
AUTHOR = {Atiyah, M. F. and Hirzebruch, F.},
TITLE = {Bott periodicity and the parallelizability
of the spheres},
JOURNAL = {Proc. Camb. Philos. Soc.},
FJOURNAL = {Proceedings of the Cambridge Philosophical
Society},
VOLUME = {57},
NUMBER = {2},
MONTH = {April},
YEAR = {1961},
PAGES = {223--226},
DOI = {10.1017/S0305004100035088},
NOTE = {MR:126282. Zbl:0108.35902.},
ISSN = {0305-0041},
}
M. F. Atiyah and F. Hirzebruch :
“Charakteristische Klassen und Anwendungen Characteristic classes and applications ],
Enseignement Math. (2)
7 : 1
(1961 ),
pp. 188–213 .
MR
154294 Zbl
0104.39801 article
People
BibTeX
@article {key154294m,
AUTHOR = {Atiyah, M. F. and Hirzebruch, F.},
TITLE = {Charakteristische {K}lassen und {A}nwendungen
[Characteristic classes and applications]},
JOURNAL = {Enseignement Math. (2)},
FJOURNAL = {L'Enseignement Math\'ematique. Revue
Internationale. IIe S\'erie},
VOLUME = {7},
NUMBER = {1},
YEAR = {1961},
PAGES = {188--213},
DOI = {10.5169/seals-37131},
NOTE = {MR:154294. Zbl:0104.39801.},
ISSN = {0013-8584},
}
M. F. Atiyah and F. Hirzebruch :
“The Riemann–Roch theorem for analytic embeddings Topology
1 : 2
(April–June 1962 ),
pp. 151–166 .
MR
148084 Zbl
0108.36402 article
Abstract
People
BibTeX
In [Borel and Serre 1958] Grothendieck formulated and proved a generalization of the Riemann–Roch theorem which we shall refer to as GRR. This theorem is concerned with a proper morphism \( f:Y\to X \) of algebraic manifolds (any ground field) and reduces to the version (HRR) given in [Hirzebruch 1956] when \( X \) is a point (and the ground field is \( \mathbb{C} \) ). It is not known whether GRR or even HRR holds for arbitrary complex manifolds. However the proof of GRR given in [Borel and Serre 1958] breaks up into two separate cases:
\( f \) is an embedding,\( f \) is a projection \( X\times P_N \to X \) , where \( P_N \) is a projective space,
and the main purpose of this paper is to give a proof of GRR in case (i) for arbitrary complex manifolds. This proof is quite different from, and in many ways simpler than, that of [Borel and Serre 1958] and, for the complex algebraic case, it gives a new proof of GRR.
@article {key148084m,
AUTHOR = {Atiyah, M. F. and Hirzebruch, F.},
TITLE = {The {R}iemann--{R}och theorem for analytic
embeddings},
JOURNAL = {Topology},
FJOURNAL = {Topology. An International Journal of
Mathematics},
VOLUME = {1},
NUMBER = {2},
MONTH = {April--June},
YEAR = {1962},
PAGES = {151--166},
DOI = {10.1016/0040-9383(65)90023-6},
NOTE = {MR:148084. Zbl:0108.36402.},
ISSN = {0040-9383},
}
M. F. Atiyah and F. Hirzebruch :
“Analytic cycles on complex manifolds Topology
1 : 1
(January–March 1962 ),
pp. 25–45 .
MR
145560 Zbl
0108.36401 article
Abstract
People
BibTeX
Let \( X \) be a complex manifold, \( Y \) a closed irreducible \( k \) -dimensional complex analytic subspace of \( X \) . Then \( Y \) defines or “carries” a \( 2k \) -dimensional integral homology class \( y \) of \( X \) , although the precise definition of \( y \) presents technical difficu1ties. A finite formal linear combination \( \sum n_iY_i \) with \( n_i \) integers and \( Y_i \) as above is called a complex analytic cycle, and the corresponding homology class \( \sum n_iY_i \) is called a complex analytic homology class. If an integral cohomology class \( u \) corresponds under Poincaré duality to a complex analytic homology class we shall say that \( u \) is a complex analytic cohomology class . The purpose of this paper is to show that a complex analytic cohomology class \( u \) satisfies certain topological conditions, independent of the complex structure of \( X \) . These conditions are that certain cohomology operations should vanish on \( u \) , for example \( \mathrm{Sq}^3u = 0 \) : they are all torsion conditions. We also produce examples to show that these conditions are not vacuous even in the restricted classes of (a) Stein manifolds and (b) projective algebraic manifolds.
@article {key145560m,
AUTHOR = {Atiyah, M. F. and Hirzebruch, F.},
TITLE = {Analytic cycles on complex manifolds},
JOURNAL = {Topology},
FJOURNAL = {Topology. An International Journal of
Mathematics},
VOLUME = {1},
NUMBER = {1},
MONTH = {January--March},
YEAR = {1962},
PAGES = {25--45},
DOI = {10.1016/0040-9383(62)90094-0},
NOTE = {MR:145560. Zbl:0108.36401.},
ISSN = {0040-9383},
}
M. Atiyah and F. Hirzebruch :
“Spin-manifolds and group actions 18–28
in
Essays on topology and related topics (Mémoires dédiés à Georges de Rham)
[Essays on topology and related topics (Memoirs dedicated to Georges de Rham) ]
(Geneva, 26–28 March 1969 ).
Edited by R. Narasimhan and A. Haefliger .
Springer (New York ),
1970 .
MR
278334 Zbl
0193.52401 incollection
People
BibTeX
@incollection {key278334m,
AUTHOR = {Atiyah, Michael and Hirzebruch, Friedrich},
TITLE = {Spin-manifolds and group actions},
BOOKTITLE = {Essays on topology and related topics
({M}\'emoires d\'edi\'es \`a {G}eorges
de {R}ham) [Essays on topology and related
topics ({M}emoirs dedicated to {G}eorges
de {R}ham)]},
EDITOR = {Narasimhan, Raghavan and Haefliger,
Andre},
PUBLISHER = {Springer},
ADDRESS = {New York},
YEAR = {1970},
PAGES = {18--28},
DOI = {10.1007/978-3-642-49197-9_3},
NOTE = {(Geneva, 26--28 March 1969). MR:278334.
Zbl:0193.52401.},
ISBN = {9783642491993},
}
M. F. Atiyah and F. Hirzebruch :
“Vector bundles and homogeneous spaces ,”
pp. 197–222
in
Algebraic topology: A student’s guide .
Edited by J. F. Adams .
London Mathematcial Society Lecture Note Series 4 .
Cambridge University Press ,
1972 .
Dedicated to Professor Marston Morse.
Republished from Differential geometry (1961)
incollection
People
BibTeX
@incollection {key46028069,
AUTHOR = {Atiyah, M. F. and Hirzebruch, F.},
TITLE = {Vector bundles and homogeneous spaces},
BOOKTITLE = {Algebraic topology: {A} student's guide},
EDITOR = {Adams, J. F.},
SERIES = {London Mathematcial Society Lecture
Note Series},
NUMBER = {4},
PUBLISHER = {Cambridge University Press},
YEAR = {1972},
PAGES = {197--222},
NOTE = {Dedicated to Professor Marston Morse.
Republished from \textit{Differential
geometry} (1961).},
ISSN = {0076-0552},
ISBN = {9780521080767},
}
M. Atiyah :
“Friedrich Hirzebruch: An appreciation ,”
pp. 1–5
in
Proceedings of the Hirzebruch 65 conference on algebraic geometry
(Ramat Gan, Israel, 2–7 May 1993 ).
Edited by M. Teicher .
Israel Mathematical Conference Proceedings 9 .
Bar-Ilan University (Ramat Gan, Israel ),
1996 .
Zbl
0834.01012 incollection
People
BibTeX
@incollection {key0834.01012z,
AUTHOR = {Atiyah, M.},
TITLE = {Friedrich {H}irzebruch: {A}n appreciation},
BOOKTITLE = {Proceedings of the {H}irzebruch 65 conference
on algebraic geometry},
EDITOR = {Teicher, Mina},
SERIES = {Israel Mathematical Conference Proceedings},
NUMBER = {9},
PUBLISHER = {Bar-Ilan University},
ADDRESS = {Ramat Gan, Israel},
YEAR = {1996},
PAGES = {1--5},
NOTE = {(Ramat Gan, Israel, 2--7 May 1993).
Zbl:0834.01012.},
ISSN = {0792-4119},
ISBN = {9789996281068},
}
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},
}
F. Hirzebruch :
“The Atiyah–Bott–Singer fixed point theorem and number theory 313–326
in
Papers dedicated to Atiyah, Bott, Hirzebruch and Singer
(Cambridge, MA, 14–16 May 1999 ).
Edited by S.-T. Yau .
Surveys in Differential Geometry 7 .
International Press (Somervile, MA ),
2000 .
MR
1919429 Zbl
1061.58022 incollection
People
BibTeX
@incollection {key1919429m,
AUTHOR = {Hirzebruch, F.},
TITLE = {The {A}tiyah--{B}ott--{S}inger fixed
point theorem and number theory},
BOOKTITLE = {Papers dedicated to {A}tiyah, {B}ott,
{H}irzebruch and {S}inger},
EDITOR = {Yau, Shing-Tung},
SERIES = {Surveys in Differential Geometry},
NUMBER = {7},
PUBLISHER = {International Press},
ADDRESS = {Somervile, MA},
YEAR = {2000},
PAGES = {313--326},
DOI = {10.4310/SDG.2002.v7.n1.a10},
NOTE = {(Cambridge, MA, 14--16 May 1999). MR:1919429.
Zbl:1061.58022.},
ISSN = {1052-9233},
ISBN = {9781571460691},
}
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},
}
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},
}
S.-T. Yau, F. E. P. Hirzebruch, M. Atiyah, M. do Carmo, R. E. Greene, W.-l. Huang, K. Reich, L. Ji, J. Li, E. Kuh, Y. R. Shen, I. M. Singer, A. Weinstein, and J. A. Wolf :
“Shiing-Shen Chern (1911–2004) Notices Am. Math. Soc.
58 : 9
(October 2011 ),
pp. 1226–1249 .
Hirzebruch’s contribution to this article was also published in Frontiers of mathematical sciences (2011)
MR
2868099 Zbl
1228.01052 article
People
BibTeX
@article {key2868099m,
AUTHOR = {Yau, Shing-Tung and Hirzebruch, Friedrich
Ernst Peter and Atiyah, Michael and
do Carmo, Manfredo and Greene, Robert
E. and Huang, Wen-ling and Reich, Karin
and Ji, Lizhen and Li, Jun and Kuh,
Ernest and Shen, Y. Ron and Singer,
Isadore M. and Weinstein, Alan and Wolf,
Joseph A.},
TITLE = {Shiing-{S}hen {C}hern (1911--2004)},
JOURNAL = {Notices Am. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical
Society},
VOLUME = {58},
NUMBER = {9},
MONTH = {October},
YEAR = {2011},
PAGES = {1226--1249},
URL = {http://www.ams.org/notices/201109/rtx110901226p.pdf},
NOTE = {Hirzebruch's contribution to this article
was also published in \textit{Frontiers
of mathematical sciences} (2011). MR:2868099.
Zbl:1228.01052.},
ISSN = {0002-9920},
}
M. Sanz-Solé, M. Atiyah, C. Bär, G.-M. Greuel, Y. I. Manin, and J.-P. Bourguignon :
“Friedrich Hirzebruch memorial session at the 6th European Congress of Mathematics: Kraków, July 5th, 2012 ,”
Eur. Math. Soc. Newsl.
2012 : 85
(September 2012 ),
pp. 12–20 .
MR
2986335 Zbl
1264.01020 article
People
BibTeX
@article {key2986335m,
AUTHOR = {Sanz-Sol\'e, Marta and Atiyah, Michael
and B\"ar, Christian and Greuel, Gert-Martin
and Manin, Yuri I. and Bourguignon,
Jean-Pierre},
TITLE = {Friedrich {H}irzebruch memorial session
at the 6th {E}uropean {C}ongress of
{M}athematics: {K}rak\'ow, July 5th,
2012},
JOURNAL = {Eur. Math. Soc. Newsl.},
FJOURNAL = {European Mathematical Society Newsletter},
VOLUME = {2012},
NUMBER = {85},
MONTH = {September},
YEAR = {2012},
PAGES = {12--20},
NOTE = {MR:2986335. Zbl:1264.01020.},
ISSN = {1027-488X},
}
M. Atiyah :
“Friedrich Ernst Peter Hirzebruch: 17 October 1927–27 May 2012 Biogr. Mem. Fellows R. Soc.
60
(December 2014 ).
article
People
BibTeX
@article {key69613074,
AUTHOR = {Atiyah, Michael},
TITLE = {Friedrich {E}rnst {P}eter {H}irzebruch:
17 {O}ctober 1927--27 {M}ay 2012},
JOURNAL = {Biogr. Mem. Fellows R. Soc.},
FJOURNAL = {Biographical Memoirs of Fellows of the
Royal Society},
VOLUME = {60},
MONTH = {December},
YEAR = {2014},
DOI = {10.1098/rsbm.2014.0010},
ISSN = {0080-4606},
}
M. Atiyah, D. Zagier, I. Manin, Yuri, G. van der Geer, J. Milnor, M. Teicher, K. Ueno, G. Segal, S. Janeczko, J.-P. Bourguignon, M. Kreck, and U. Schmickler-Hirzebruch :
“Friedrich Hirzebruch (1927–2012) Notices Am. Math. Soc.
61 : 7
(August 2014 ),
pp. 706–727 .
article
People
BibTeX
@article {key26518992,
AUTHOR = {Atiyah, Michael and Zagier, Don and
Manin, Yuri, I. and van der Geer, Gerard
and Milnor, John and Teicher, Mina and
Ueno, Kenji and Segal, Graeme and Janeczko,
Stanis\l aw and Bourguignon, Jean-Pierre
and Kreck, Matthias and Schmickler-Hirzebruch,
Ulrike},
TITLE = {Friedrich {H}irzebruch (1927--2012)},
JOURNAL = {Notices Am. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical
Society},
VOLUME = {61},
NUMBER = {7},
MONTH = {August},
YEAR = {2014},
PAGES = {706--727},
URL = {http://www.ams.org/notices/201407/rnoti-p706.pdf},
ISSN = {0002-9920},
}
