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Article
Symmetries and exotic smooth structures on a K3 surface
JOURNAL OF TOPOLOGY
  • WM Chen, University of Massachusetts - Amherst
  • S Kwasik
Publication Date
2008
Abstract
Smooth and symplectic symmetries of an infinite family of distinct exotic K3 surfaces are studied, and a comparison with the corresponding symmetries of the standard K3 is made. The action on the K3 lattice induced by a smooth finite group action is shown to be strongly restricted, and, as a result, the nonsmoothability of actions induced by a holomorphic automorphism of prime order at least 7 is proved, and the nonexistence of smooth actions by several K3 groups is established (included among which is the binary tetrahedral group T24 that has the smallest order). Concerning symplectic symmetries, the fixed-point set structure of a symplectic cyclic action of prime order at least 5 is explicitly determined, provided that the action is homologically nontrivial.
Comments

This is the pre-published version harvested from ArXiv. The published version is located at http://jtopol.oxfordjournals.org/content/1/4/923.refs

Pages
923-962
Citation Information
WM Chen and S Kwasik. "Symmetries and exotic smooth structures on a K3 surface" JOURNAL OF TOPOLOGY Vol. 1 Iss. 4 (2008)
Available at: http://works.bepress.com/weiminchen_chen/3/