Free loop space and homology

Details Free loop space and homology Free loop space and homology

2011-10-03

arxiv.org/abs/1110.0405v1

Mathematics

Algebraic Topology

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

Scientific paper

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.

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