Symplectic symmetries of 4-manifolds

• Autores: Weimin Chen, Slawomir Kwasik
• Localización: Topology, ISSN 0040-9383, Vol. 46, Nº 2, 2007, págs. 103-128
• Idioma: inglés
• DOI: 10.1016/j.top.2006.12.003
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• Resumen

  • A study of symplectic actions of a finite group on smooth 4-manifolds is initiated. The central new idea is the use of -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 surface (in analogy with holomorphic automorphisms). Various examples and comments illustrating our considerations are also included