The homology of path spaces and Floer homology with conormal boundary conditions

TL;DR

This paper introduces a Floer complex for Hamiltonian orbits with conormal boundary conditions on cotangent bundles and proves its homology matches the singular homology of associated path spaces.

Contribution

It defines a new Floer complex for non-local conormal boundary conditions and establishes an isomorphism with the singular homology of relevant path spaces.

Findings

Floer complex for Hamiltonian orbits with conormal boundary conditions

Homology of the Floer complex is isomorphic to singular homology of path spaces

Provides a new link between Floer homology and classical topology

Abstract

We define the Floer complex for Hamiltonian orbits on the cotangent bundle of a compact manifold satisfying non-local conormal boundary conditions. We prove that the homology of this chain complex is isomorphic to the singular homology of the natural path space associated to the boundary conditions.