The homology of path spaces and Floer homology with conormal boundary   conditions
  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. 
Alberto Abbondandolo, Alessandro Portaluri, Matthias Schwarz