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 $\phi$ be an exact symplectomorphism of $M$ which, near infinity, is equal to either the identity or the symplectization of a contactomorphism $\hat{\phi}$ such that neither $\hat{\phi}$ nor $\hat{\phi}^2$ 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 $\mathit{HF}(\phi^2)\otimes \mathbb Z_2((\theta))$ to $\mathit{HF}(\phi)\otimes \mathbb Z_2((\theta))$.