Seiberg–Witten vanishing theorem for S¹-manifolds with fixed points

Scott Baldridge

Vol. 217 (2004), No. 1, 1–10

DOI: 10.2140/pjm.2004.217.1

Abstract

We show that the Seiberg–Witten invariant is zero for all smooth 4-manifolds with b₊>1 that admit circle actions having at least one fixed point. We also show that all symplectic 4-manifolds that admit (possibly nonsymplectic) circle actions with fixed points are rational or ruled, and thus admit a symplectic circle action.

Milestones

Received: 15 March 2004

Published: 1 November 2004