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Geometric and Functional Analysis

, Volume 20, Issue 6, pp 1464–1501 | Cite as

Localization for Involutions in Floer Cohomology

  • Paul Seidel
  • Ivan SmithEmail author
Article

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.

Keywords and phrases

Floer cohomology symplectic group actions Khovanov homology Heegaard Floer cohomology 

2010 Mathematics Subject Classification

53D35 53D40 57M27 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.MITCambridgeUSA
  2. 2.Centre for Mathematical SciencesCambridgeUK

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