Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

Received:
May 5, 2008
Published:
May 14, 2008
MSC Codes:
53D40, 57R58

Related publications

inJournal
2010 Repository Open Access
Alberto Abbondandolo and Matthias Schwarz

Floer homology of cotangent bundles and the loop product

In: Geometry and topology, 14 (2010) 3, pp. 1569-1722