Viterbo's transfer morphism for symplectomorphisms

TL;DR

This paper develops a new transfer morphism in Floer homology for symplectomorphisms of Liouville domains and uses it to prove that certain Dehn twists have infinite order in the symplectic mapping class group.

Contribution

It introduces an analogue of Viterbo's transfer morphism for Floer homology of automorphisms in Liouville domains, advancing symplectic topology methods.

Findings

Dehn-Seidel twists along Lagrangian spheres have infinite order in high-dimensional Liouville domains.

Constructed a transfer morphism for Floer homology of automorphisms.

Applied the morphism to prove properties of symplectic mapping class groups.

Abstract

We construct an analogue of Viterbo's transfer morphism for Floer homology of an automorphism of a Liouville domain. As an application we prove that the Dehn-Seidel twist along any Lagrangian sphere in a Liouville domain of dimension $\geqslant 4$ has infinite order in the symplectic mapping class group.