arXiv:1110.0405 Abstract | arXiv Analytics

arXiv:1110.0405 [math.AT]Abstract References Reviews Resources

Free loop space and homology

Published 2011-10-03Version 1

The aim of this paper is to explain the relationship between the (co)homology of the free loop space and the Hochschild homology of its singular cochain algebra. We introduce all the relevant technical tools, namely simplicial and cyclic objects, and we provide the various steps of the proofs, which are scattered around in the literature. This paper can be seen as a companion to the paper "Cyclic homology and equivariant homology" by J.D.S. Jones dealing with the cyclic case.

Comments: 20 p. Part of a book on symplectic geometry edited by Alex Oancea

Categories: math.AT, math.DG

Subjects: 19D55, 55P35

Keywords: free loop space, singular cochain algebra, relevant technical tools, hochschild homology, cyclic objects

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