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.
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Seidel, P., Smith, I. Localization for Involutions in Floer Cohomology. Geom. Funct. Anal. 20, 1464–1501 (2010). https://doi.org/10.1007/s00039-010-0099-y
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DOI: https://doi.org/10.1007/s00039-010-0099-y