Fixed point Floer cohomology of disjoint Dehn twists on a w+-monotone manifold with rational symplectic form

TL;DR

This paper explicitly computes the Floer cohomology for disjoint Dehn twists in a monotone rational symplectic manifold and introduces a vanishing class in fixed point Floer cohomology, with implications for Seidel's sequence.

Contribution

It provides an explicit description of Floer cohomology for Dehn twists and defines a new vanishing class in fixed point Floer cohomology within monotone symplectic manifolds.

Findings

Explicit Floer cohomology description for disjoint Dehn twists

Definition of a vanishing class in fixed point Floer cohomology

Framework for future geometric proofs of Seidel's long exact sequence

Abstract

We give an explicit description of the Floer cohomology of a family of Dehn twists about disjoint Lagrangian spheres in a w+ - monotone rational symplectic manifold. As a byproduct of our framework, in a monotone symplectic manifold we are able to define a class in the fixed point Floer cohomology of a Dehn twist by counting half strips bound to the given Lagrangian sphere and prove it must vanish. In subsequent work we plan on using this vanishing result to give a new geometric proof of Seidel's long exact sequence.