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arXiv:math/0201034 [math.GT]AbstractReferencesReviewsResources

Seiberg-Witten vanishing theorem for $S^1$-manifolds with fixed points

Scott Baldridge

Published 2002-01-07, updated 2002-02-10Version 2

In this paper we show that the Seiberg--Witten invariant is zero for all smooth 4--manifolds with $b_+{>}1$ which admit circle actions that have at least one fixed point. Furthermore, we show that all symplectic 4--manifolds which admit circle actions with fixed points are rational or ruled, and thus admit a symplectic circle action.

Comments: Includes new theorem classifying symplectic 4-manifolds with circle actions having fixed points. Minor updates to existing proofs to reflect the new theorem. 7 pages, 2 figures
Categories: math.GT, math.SG
Subjects: 57R57, 57M60
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