R. Kirby and P. Melvin :
“Slice knots and property R Invent. Math.
45 : 1
(1978 ),
pp. 57–59 .
MR
0467754 Zbl
0377.55002
People
BibTeX
@article {key0467754m,
AUTHOR = {Kirby, Robion and Melvin, Paul},
TITLE = {Slice knots and property {R}},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {45},
NUMBER = {1},
YEAR = {1978},
PAGES = {57--59},
NOTE = {Available at
http://dx.doi.org/10.1007/BF01406223.
MR 57 \#7606. Zbl 0377.55002.},
ISSN = {0020-9910},
}
R. Kirby and P. Melvin :
“Evaluations of the 3-manifold invariants of Witten and
Reshetikhin–Turaev for \( \mathrm{sl}(2,\mathbf{C}) \) ,”
pp. 101–114
in
Geometry of low-dimensional manifolds
(Durham, 1989 ),
vol. 2 .
Edited by S. K. Donaldson and C. B. Thomas .
London Math. Soc. Lecture Note Ser. 151 .
Cambridge Univ. Press ,
1990 .
MR
1171911 Zbl
0756.57006
People
BibTeX
@incollection {key1171911m,
AUTHOR = {Kirby, Robion and Melvin, Paul},
TITLE = {Evaluations of the {3}-manifold invariants
of {W}itten and {R}eshetikhin--{T}uraev
for \$\mathrm{sl}(2,\mathbf{C})\$},
BOOKTITLE = {Geometry of low-dimensional manifolds},
EDITOR = {Donaldson, S. K. and Thomas, C. B.},
VOLUME = {2},
SERIES = {London Math. Soc. Lecture Note Ser.},
NUMBER = {151},
PUBLISHER = {Cambridge Univ. Press},
YEAR = {1990},
PAGES = {101--114},
NOTE = {(Durham, 1989). MR 93e:57027. Zbl 0756.57006.},
}
R. Kirby and P. Melvin :
“The 3-manifold invariants of Witten and
Reshetikhin–Turaev for \( \mathrm{sl}(2,\mathbf{C}) \) Invent. Math.
105 : 3
(1991 ),
pp. 473–545 .
MR
1117149 Zbl
0745.57006
People
BibTeX
@article {key1117149m,
AUTHOR = {Kirby, Robion and Melvin, Paul},
TITLE = {The {3}-manifold invariants of {W}itten
and {R}eshetikhin--{T}uraev for \$\mathrm{sl}(2,\mathbf{C})\$},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {105},
NUMBER = {3},
YEAR = {1991},
PAGES = {473--545},
NOTE = {Available at
http://dx.doi.org/10.1007/BF01232277.
MR 92e:57011. Zbl 0745.57006.},
ISSN = {0020-9910},
CODEN = {INVMBH},
}
R. Kirby, P. Melvin, and X. Zhang :
“Quantum invariants at the sixth root of unity Comm. Math. Phys.
151 : 3
(1993 ),
pp. 607–617 .
MR
1207268 Zbl
0779.57007
People
BibTeX
@article {key1207268m,
AUTHOR = {Kirby, Robion and Melvin, Paul and Zhang,
Xingru},
TITLE = {Quantum invariants at the sixth root
of unity},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {151},
NUMBER = {3},
YEAR = {1993},
PAGES = {607--617},
NOTE = {Available at
http://projecteuclid.org/euclid.cmp/1104252242.
MR 95f:57037. Zbl 0779.57007.},
ISSN = {0010-3616},
CODEN = {CMPHAY},
}
R. Kirby and P. Melvin :
“Dedekind sums, \( \mu \)-invariants and the signature cocycle Math. Ann.
299 : 2
(1994 ),
pp. 231–267 .
MR
1275766 Zbl
0809.11027
People
BibTeX
@article {key1275766m,
AUTHOR = {Kirby, Robion and Melvin, Paul},
TITLE = {Dedekind sums, \$\mu\$-invariants and
the signature cocycle},
JOURNAL = {Math. Ann.},
FJOURNAL = {Mathematische Annalen},
VOLUME = {299},
NUMBER = {2},
YEAR = {1994},
PAGES = {231--267},
NOTE = {Available at
http://dx.doi.org/10.1007/BF01459782.
MR 95h:11042. Zbl 0809.11027.},
ISSN = {0025-5831},
CODEN = {MAANA},
}
R. Kirby and P. Melvin :
“Canonical framings for 3-manifolds ,”
pp. 89–115
in
Proceedings of 6th Gökova Geometry-Topology
Conference ,
published as Turkish J. Math.
23 : 1 .
1999 .
MR
1701641 Zbl
0947.57020
People
BibTeX
@article {key1701641m,
AUTHOR = {Kirby, Rob and Melvin, Paul},
TITLE = {Canonical framings for {3}-manifolds},
JOURNAL = {Turkish J. Math.},
FJOURNAL = {Turkish Journal of Mathematics},
VOLUME = {23},
NUMBER = {1},
YEAR = {1999},
PAGES = {89--115},
NOTE = {\textit{Proceedings of 6th {G}\"okova
{G}eometry-{T}opology {C}onference}.
MR 2000k:57026. Zbl 0947.57020.},
ISSN = {1300-0098},
}
R. Kirby and P. Melvin :
“The \( E_8 \)-manifold, singular fibers and handlebody
decompositions 233–258
in
Proceedings of the Kirbyfest
(Berkeley, CA, 1998 ).
Edited by J. Hass and M. Scharlemann .
Geom. Topol. Monogr. 2 .
Geom. Topol. Publ., Coventry ,
1999 .
MR
1734411 Zbl
0959.57020
People
BibTeX
@inproceedings {key1734411m,
AUTHOR = {Kirby, Robion and Melvin, Paul},
TITLE = {The \$E_8\$-manifold, singular fibers
and handlebody decompositions},
BOOKTITLE = {Proceedings of the {K}irbyfest},
EDITOR = {Hass, Joel and Scharlemann, Martin},
SERIES = {Geom. Topol. Monogr.},
NUMBER = {2},
PUBLISHER = {Geom. Topol. Publ., Coventry},
YEAR = {1999},
PAGES = {233--258},
NOTE = {(Berkeley, CA, 1998). Available at
http://dx.doi.org/10.2140/gtm.1999.2.233.
MR 2000j:57051. Zbl 0959.57020.},
}
R. Kirby and P. Melvin :
“Local surgery formulas for quantum invariants and the Arf
invariant 213–233
in
Proceedings of the Casson Fest .
Edited by C. Gordon and Y. Rieck .
Geom. Topol. Monogr. 7 .
Geom. Topol. Publ. (Coventry ),
2004 .
MR
2172485 Zbl
1087.57006
People
BibTeX
@inproceedings {key2172485m,
AUTHOR = {Kirby, Robion and Melvin, Paul},
TITLE = {Local surgery formulas for quantum invariants
and the {A}rf invariant},
BOOKTITLE = {Proceedings of the {C}asson {F}est},
EDITOR = {Gordon, Cameron and Rieck, Yoav},
SERIES = {Geom. Topol. Monogr.},
NUMBER = {7},
PUBLISHER = {Geom. Topol. Publ.},
ADDRESS = {Coventry},
YEAR = {2004},
PAGES = {213--233},
NOTE = {Available at
http://dx.doi.org/10.2140/gtm.2004.7.213.
MR 2006g:57023. Zbl 1087.57006.},
}
R. Kirby, P. Melvin, and P. Teichner :
“Cohomotopy sets of 4-manifolds 161–190
in
Proceedings of the Freedman Fest
(Santa Barbara, CA, 15–17 April 2011 and Berkeley, CA, 6–10 June 2011 ).
Edited by R. Kirby, V. Krushkal, and Z. Wang .
Geometry & Topology Monographs 18 .
Geometry & Topology Publications (Coventry, UK ),
2012 .
MR
3084237 Zbl
1273.57012 ArXiv
1203.1608 incollection
Abstract
People
BibTeX
Elementary geometric arguments are used to compute the group of homotopy classes of maps from a 4-manifold \( X \) to the 3-sphere, and to enumerate the homotopy classes of maps from \( X \) to the 2-sphere. The former completes a project initiated by Steenrod in the 1940s, and the latter provides geometric arguments for and extensions of recent homotopy theoretic results of Larry Taylor. These two results complete the computation of all the cohomotopy sets of closed oriented 4-manifolds and provide a framework for the study of Morse 2-functions on 4-manifolds, a subject that has garnered considerable recent attention.
@incollection {key3084237m,
AUTHOR = {Kirby, Robion and Melvin, Paul and Teichner,
Peter},
TITLE = {Cohomotopy sets of 4-manifolds},
BOOKTITLE = {Proceedings of the {F}reedman {F}est},
EDITOR = {Kirby, Rob and Krushkal, Vyacheslav
and Wang, Zhenghan},
SERIES = {Geometry \& Topology Monographs},
NUMBER = {18},
PUBLISHER = {Geometry \& Topology Publications},
ADDRESS = {Coventry, UK},
YEAR = {2012},
PAGES = {161--190},
DOI = {10.2140/gtm.2012.18.161},
NOTE = {(Santa Barbara, CA, 15--17 April 2011
and Berkeley, CA, 6--10 June 2011).
ArXiv:1203.1608. MR:3084237. Zbl:1273.57012.},
ISSN = {1464-8989},
}
