On product structures in Floer homology of cotangent bundles

Floer homology of cotangent bundles and the loop product

We prove that the pair-of-pants product on the Floer homology of the cotangent bundle of a compact manifold M corresponds to the Chas-Sullivan loop product on the singular homology of the loop space of M . We also prove related results concerning the Floer homological interpretation of the Pontrjagin product and of the Serre fibration. The techniques include a Fredholm theory for Cauchy-Riemann...

Mathematik in den Naturwissenschaften Leipzig Floer homology of cotangent bundles and the loop product

homology of cotangent bundles and the loop product

We prove that the pair-of-pants product on the Floer homology of the cotangent bundle of a compact manifold M corresponds to the Chas-Sullivan loop product on the singular homology of the loop space of M. We also prove related results concerning the Floer homo-logical interpretation of the Pontrjagin product and of the Serre fibration. The techniques include a Fredholm theory for Cauchy-Riemann...

On the Floer homology of cotangent bundles

This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle T M of a compact orientable manifold M . The first result is a new L estimate for the solutions of the Floer equation, which allows to deal with a larger and more natural class of Hamiltonians. The second and main result is a new construction of the isomorphism between the Fl...

Three approaches towards Floer homology of cotangent bundles

Consider the cotangent bundle of a closed Riemannian manifold and an almost complex structure close to the one induced by the Riemannian metric. For Hamiltonians which grow for instance quadratically in the fibers outside of a compact set, one can define Floer homology and show that it is naturally isomorphic to singular homology of the free loop space. We review the three isomorphisms construc...