Symmetric symplectic homotopy K3 surfaces

Details Symmetric symplectic homotopy K3 surfaces Symmetric symplectic homotopy K3 surfaces

2007-09-16

arxiv.org/abs/0709.2448v2

Mathematics

Geometric Topology

30 pages, 1 figure, with a slightly changed title. Accepted for publication by the Journal of Topology

Scientific paper

A study on the relation between the smooth structure of a symplectic homotopy K3 surface and its symplectic symmetries is initiated. A measurement of exoticness of a symplectic homotopy K3 surface is introduced, and the influence of an effective action of a K3 group via symplectic symmetries is investigated. It is shown that an effective action by various maximal symplectic K3 groups forces the corresponding homotopy K3 surface to be minimally exotic with respect to our measure. (However, the standard K3 is the only known example of such minimally exotic homotopy K3 surfaces.) The possible structure of a finite group of symplectic symmetries of a minimally exotic homotopy K3 surface is determined and future research directions are indicated.

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