Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
MiS Preprint
41/2008
Floer homology of cotangent bundles and the loop product
Alberto Abbondandolo and Matthias Schwarz
Abstract
In a previous paper we constructed an isomorphism between Floer homology on the cotangent bundle of an oriented, closed manifold $M$ for a suitable class of Hamiltonians of fibrewise quadratic type, and the homology of the free loop space of $M$. In this paper, we show that this isomorphism is also a ring isomorphism if we endow Flow homology with its natural pair-of-pants ring structure and the free loop space homology with the Chas-Sullivan loop product.
In particular, we show that also the pair-of-pants product factors through a variant of Floer homology associated to figure-8-loops, compatible with the factorization of the Chas-Sullivan loop product. This makes repeated use of Lagrangian boundary conditions of conormal type.
