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

2002/01/07 by Scott Baldridge, Baldridge, Scott
Mathematics · #57M60 #57R57 #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.GT #math.SG #msc:57M60 #msc:57R57

paper · pdf · doi:10.48550/arxiv.math/0201034

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

arxiv created 2002/02/10 · arxiv updated 2009/11/30

Abstract

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.

Related

• Seiberg-Witten invariants of 4-manifolds with free circle actions
• Seiberg-Witten invariants, orbifolds, and circle actions
• Seifert fibered four-manifolds with nonzero Seiberg-Witten invariant
• Symplectic 4-manifolds with fixed point free circle actions
• Hyperbolic four-manifolds with vanishing Seiberg-Witten invariants