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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.
Available at: http://works.bepress.com/weiminchen_chen/7/
This is the pre-published version harvested from ArXiv. The published version is located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V1J-4MRN9P1-1&_user=1516330&_coverDate=03%2F31%2F2007&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1699917547&_rerunOrigin=google&_acct=C000053443&_version=1&_urlVersion=0&_userid=1516330&md5=4abbee1df8f6244c3d8dd0a5939aa1ad&searchtype=a