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Notes on homology cobordisms of plumbed homology 3-spheres
Author(s):
Nikolai
Saveliev
Journal:
Proc. Amer. Math. Soc.
126
(1998),
2819-2825.
MSC (1991):
Primary 57M25, 57R80
MathSciNet review:
1451828
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Abstract:
The gauge-theoretical invariants of Donaldson and Seiberg-Witten are used to detect some infinite order elements in the homology cobordism group of integral homology 3-spheres.
References:
- [A]
- S. Akbulut, Lectures on Seiberg-Witten Invariants, Turkish J. Math. 20 (1996), 95-118. MR 97g:57038
- [D]
- S. Donaldson, The orientation of Yang-Mills moduli spaces and 4-manifold topology, J. Diff. Geom. 26 (1987), 397-428. MR 88j:57020
- [Du]
- N. Duchon, Involutions of plumbed manifolds, Ph.D. Thesis, University of Maryland, College Park, 1982.
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- D. Eisenbud, W. Neumann, Three-dimensional Link Theory and Invariants of Plane Curve Singularities, Annals of Math. Studies 110, Princeton, 1985. MR 87g:57007
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- R. Fintushel, R. Stern, Pseudofree orbifolds, Ann. Math. 122 (1985), 335-364. MR 87a:57027
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- M. Furuta, Monopole equation and the 11/8 conjecture, Preprint.
- [N]
- W. Neumann, An invariant of plumbed homology spheres, Lecture Notes in Math. 788, Springer-Verlag, Berlin and New-York, 1980, 125-144. MR 82j:57033
- [NR]
- W. Neumann, F. Raymond, Seifert manifolds, plumbing,
 -invariant and orientation reversing maps, Lecture Notes in Math. , Springer-Verlag, Berlin and New-York, 1978, 163-196. MR 80e:57008 - [NW]
- W. Neumann, J. Wahl, Casson invariant of links of singularities, Comm. Math. Helv. 65 (1990), 58-78. MR 91c:57022
- [S1]
- N. Saveliev, Dehn surgery along torus knots, Topology and Its Appl. (to appear).
- [S2]
- N. Saveliev, Floer homology and 3-manifold invariants, Ph.D. Thesis, University of Oklahoma, Norman, 1995.
- [S]
- L. Siebenmann, On vanishing of the Rohlin invariant and nonfinitely amphicheiral homology 3-spheres, Lecture Notes in Math. 788, Springer-Verlag, Berlin and New-York, 1980, 172-222. MR 81k:57011
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Additional Information:
Nikolai
Saveliev
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email:
saveliev@math.lsa.umich.edu
DOI:
10.1090/S0002-9939-98-04359-7
PII:
S 0002-9939(98)04359-7
Keywords:
Homology 3-sphere,
homology cobordism,
gauge theory
Received by editor(s):
November 19, 1996
Received by editor(s) in revised form:
February 11, 1997
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
1998,
American Mathematical Society
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