Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Seiberg-Witten invariants for manifolds diffeomorphic outside a circle

Author(s): Stefano Vidussi
Journal: Proc. Amer. Math. Soc. 129 (2001), 2489-2496.
MSC (2000): Primary 57R57; Secondary 57Mxx
Posted: December 28, 2000
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: In this paper we prove that simple type four manifolds with $b_{2}^{+}>1$which are diffeomorphic outside a point or outside a wedge of circles have the same Seiberg-Witten invariants, excluding the use of these invariants to detect eventual inequivalent smooth structures.


References:

1.
S.Demichelis, On Manifolds Diffeomorphic on the Complement of a Point, Rend.Mat.Acc. Lincei s.9,v.2 (1991), pp. 229-233. MR 92k:57060
2.
S.Donaldson, P.Kronheimer, The Geometry of Four Manifolds, Oxford Math.Monographs, 1990. MR 92a:57036
3.
S.Donaldson, D.Sullivan, Quasiconformal Four Manifolds, Acta Math.163 (1989), pp. 181-252. MR 91d:57012
4.
R.Fintushel, R.Stern, 2-Torsion Instanton Invariants, J.Am.Math.Soc. 6 (1993), pp. 299-339. MR 93f:57038
5.
R.Fintushel, R.Stern, Immersed Spheres in 4-Manifolds and the Immersed Thom Conjecture, Turk.J.Math. 19 (1995), pp. 145-157. MR 96j:57036
6.
P.Kronheimer, T.Mrowka, The Genus of Embedded Surfaces in the Projective Plane, Math.Res.Lett. 1 (1994), pp. 797-808. MR 96a:57073
7.
J.Morgan, T.Mrowka, D.Ruberman, The ${\mathcal L}^{2}$-Moduli Space and a Vanishing Theorem for Donaldson Polynomial Invariants, Series in Geometry and Topology, vol. 2, International Press Inc., 1994. MR 95h:57039
8.
J.Morgan, Z.Szabó, C.Taubes, A Product Formula for Seiberg-Witten Invariants and the Generalized Thom Conjecture, J.Diff.Geom. 44 (1996), pp. 706-788. MR 97m:57052
9.
C.Taubes, Self-dual Yang-Mills Connections on non Self-dual 4-Manifolds, J.Diff.Geom. 17 (1982), pp. 139-170. MR 83i:53055
10.
S.Vidussi, Seiberg-Witten Theory for Four Manifolds Decomposed Along a Three Manifold of Positive Scalar Curvature, Prépublication École Polytechnique 99-5 (1999).

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 57R57, 57Mxx

Retrieve articles in all Journals with MSC (2000): 57R57, 57Mxx


Additional Information:

Stefano Vidussi
Affiliation: Centre de Mathématiques, UMR 7640 du CNRS, École Polytechnique, 91128 Palaiseau Cedex, France
Address at time of publication: Department of Mathematics, University of California, Irvine, California 92697
Email: svidussi@math.uci.edu

DOI: 10.1090/S0002-9939-00-05904-9
PII: S 0002-9939(00)05904-9
Keywords: Seiberg-Witten invariants, smooth topology of four manifolds
Received by editor(s): August 27, 1999
Received by editor(s) in revised form: December 10, 1999
Posted: December 28, 2000
Additional Notes: The author would like to thank Stefano Demichelis for several discussions.
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 2000, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google