English

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 b+>1b_+{>}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.

Keywords

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

R2 v1 2026-07-22T16:42:31.968Z