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arXiv · 2203.04465

A cocyclic construction of $S^1$-equivariant homology and application to string topology

Yi Wang
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Abstract

Given a space with a circle action, we study certain cocyclic chain complexes and prove a theorem relating cyclic homology to $S^1$-equivariant homology, in the spirit of celebrated work of Jones. As an application, we describe a chain level refinement of the gravity algebra structure on the (negative) $S^1$-equivariant homology of the free loop space of a closed oriented smooth manifold, based on work of Irie on chain level string topology and work of Ward on an $S^1$-equivariant version of operadic Deligne's conjecture.

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Yi Wang. 2022-03-09. A cocyclic construction of $S^1$-equivariant homology and application to string topology. https://doi.org/10.4171/jncg%2F545

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