Skip to main content
Symplectic symmetries of 4-manifolds
  • WM Chen, University of Massachusetts - Amherst
  • S Kwasik
Publication Date

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 . 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.

Citation Information
WM Chen and S Kwasik. "Symplectic symmetries of 4-manifolds" TOPOLOGY Vol. 46 Iss. 2 (2007)
Available at: