A spectral sequence of the Floer cohomology of symplectomorphisms of trivial polarization class

Abstract

Let $M$ be an exact symplectic manifold equal to a symplectization near infinity and having stably trivializable tangent bundle, and $\varphi$ be an exact symplectomorphism of $M$ which, near infinity, is equal to either the identity or the symplectization of a contactomorphism $\hat{\varphi }$ such that neither $\hat{\varphi }$ nor ${\hat{\varphi }}^2$ has fixed points. We give conditions under which Seidel and Smith's localization theorem for Lagrangian Floer cohomology implies the existence of a spectral sequence from $HF({\varphi }^2)\otimes {\mathbb{Z}}_2((\theta ))$ to $HF(\varphi )\otimes {\mathbb{Z}}_2((\theta ))$.

This is the final version published by IMRN. The most significant change is a correction to an error in the proof of Proposition 3.2 pointed out by the referee. Small updates also to orthography and exposition

References in corpus (3)

• Symplectic cohomology and duality for the wrapped Fukaya category
• Quilted Floer Cohomology
• Dehn twists and free subgroups of symplectic mapping class groups

Cited by in corpus (3)

• A simplicial construction of G-equivariant Floer homology
• On the iterated Hamiltonian Floer homology
• Equivariant Lagrangian Floer cohomology via semi-global Kuranishi structures