Localization for involutions in Floer cohomology
arXiv:1002.2648
Abstract
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.
41 pages, no figures. Version 2 corrects an erroneous argument in Section 4 (the main results are unaffected). Version 3 has minor expository changes