Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Notes on homology cobordisms
of plumbed homology 3-spheres

Author: Nikolai Saveliev
Journal: Proc. Amer. Math. Soc. 126 (1998), 2819-2825
MSC (1991): Primary 57M25, 57R80
MathSciNet review: 1451828
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [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.
  • [EN] D. Eisenbud, W. Neumann, Three-dimensional Link Theory and Invariants of Plane Curve Singularities, Annals of Math. Studies 110, Princeton, 1985. MR 87g:57007
  • [FS] R. Fintushel, R. Stern, Pseudofree orbifolds, Ann. Math. 122 (1985), 335-364. MR 87a:57027
  • [F] 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, $\mu$-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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57M25, 57R80

Retrieve articles in all journals with MSC (1991): 57M25, 57R80

Additional Information

Nikolai Saveliev

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
Article copyright: © Copyright 1998 American Mathematical Society