Handle attaching in wrapped Floer homology and brake orbits in classical Hamiltonian systems

TL;DR

This paper proves the existence of brake orbits in classical Hamiltonian systems using Floer theory by computing wrapped Floer homology and demonstrating its invariance under handle attaching.

Contribution

It introduces an open string analogue of symplectic homology for domains in cotangent bundles and shows its invariance under handle attaching, advancing Floer theory applications.

Findings

Established existence of brake orbits using Floer homology techniques

Computed wrapped Floer homology for specific cotangent bundle domains

Proved invariance of wrapped Floer homology under handle attaching

Abstract

The objective of this note is to prove an existence result for brake orbits in classical Hamiltonian systems (which was first proved by S.V.Bolotin) by using Floer theory. To this end, we compute an open string analogue of symplectic homology (so called wrapped Floer homology) of some domains in cotangent bundles, which appear naturally in the study of classical Hamiltonian systems. The main part of the computations is to show invariance of wrapped Floer homology under certain handle attaching to domains.