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Localization for Involutions in Floer Cohomology

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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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Authors and Affiliations

  1. MIT, Room 2-270, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    Paul Seidel

  2. Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB, UK

    Ivan Smith

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  1. Paul Seidel
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  2. Ivan Smith
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Correspondence to Ivan Smith.

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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

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