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

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

2002-01-07

arxiv.org/abs/math/0201034v2

Mathematics

Geometric Topology

Includes new theorem classifying symplectic 4-manifolds with circle actions having fixed points. Minor updates to existing pro

Scientific paper

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.

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