Floer homology of cotangent bundles and the loop product

Abstract

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 operators with jumping Lagrangian boundary conditions of conormal type, and a new cobordism argument replacing the standard gluing technique.

Fully revised version

References in corpus (2)

• Functors and Computations in Floer homology with Applications Part II
• Open-Closed String Topology via Fat Graphs

Cited by in corpus (6)

• Local Floer Homology and the Action Gap
• Local Floer homology and infinitely many simple Reeb orbits
• Compactness for holomorphic curves with switching Lagrangian boundary conditions
• A smooth pseudo-gradient for the Lagrangian action functional
• Conley Conjecture for Negative Monotone Symplectic Manifolds
• The homology of path spaces and Floer homology with conormal boundary conditions