Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4657694 | Topology | 2007 | 26 Pages |
Abstract
A study of symplectic actions of a finite group G on smooth 4-manifolds is initiated. The central new idea is the use of G-equivariant Seiberg-Witten-Taubes theory in studying the structure of the fixed-point set of these symmetries. The main result in this paper is a complete description of the fixed-point set structure (and the action around it) of a symplectic cyclic action of prime order on a minimal symplectic 4-manifold with c12=0. Comparison of this result with the case of locally linear topological actions is made. As an application of these considerations, the triviality of many such actions on a large class of 4-manifolds is established. In particular, we show the triviality of homologically trivial symplectic symmetries of a K3 surface (in analogy with holomorphic automorphisms). Various examples and comments illustrating our considerations are also included.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Weimin Chen, Slawomir Kwasik,