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arXiv · 1409.6009

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

Kristen Hendricks
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Abstract

Let $M$ be an exact symplectic manifold equal to a symplectization near infinity and having stably trivializable tangent bundle, and $ϕ$ be an exact symplectomorphism of $M$ which, near infinity, is equal to either the identity or the symplectization of a contactomorphism $\hatϕ$ such that neither $\hatϕ$ nor $\hatϕ^2$ 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 $\mathit{HF}(ϕ^2)\otimes \mathbb Z_2((θ))$ to $\mathit{HF}(ϕ)\otimes \mathbb Z_2((θ))$.

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Kristen Hendricks. 2016-06-17. A spectral sequence of the Floer cohomology of symplectomorphisms of trivial polarization class. https://doi.org/10.1093/imrn%2Frnw061

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