Localization for involutions in Floer cohomology

Details Localization for involutions in Floer cohomology Localization for involutions in Floer cohomology

2010-02-12

arxiv.org/abs/1002.2648v3

Mathematics

Symplectic Geometry

41 pages, no figures. Version 2 corrects an erroneous argument in Section 4 (the main results are unaffected). Version 3 has m

Scientific paper

We consider Lagrangian Floer cohomology for a pair of Lagrangian submanifolds in a symplectic manifold M. Suppose that M carries a symplectic involution, which preserves both submanifolds. Under various topological hypotheses, we prove a localization theorem for Floer cohomology, which implies a Smith-type inequality for the Floer cohomology groups in M and its fixed point set. Two applications to symplectic Khovanov cohomology are included.

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