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.

Locations

• arXiv (Cornell University) - View - PDF
• CiteSeer X (The Pennsylvania State University) - View - PDF
• Project Euclid (Cornell University) - View - PDF
• Geometry & Topology - View - PDF