Seiberg-Witten vanishing theorem for $S^1$-manifolds with fixed points
Geometric Topology
2007-05-23 v2 Symplectic Geometry
Abstract
In this paper we show that the Seiberg--Witten invariant is zero for all smooth 4--manifolds with 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.
Cite
@article{arxiv.math/0201034,
title = {Seiberg-Witten vanishing theorem for $S^1$-manifolds with fixed points},
author = {Scott Baldridge},
journal= {arXiv preprint arXiv:math/0201034},
year = {2007}
}
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