A cocyclic construction of -equivariant homology and application to string topology

  • Yi Wang

    Purdue University West Lafayette, United States of America
A cocyclic construction of $S^1$-equivariant homology and application to string topology cover
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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 -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) -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 -equivariant version of operadic Deligne’s conjecture.

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Yi Wang, A cocyclic construction of -equivariant homology and application to string topology. J. Noncommut. Geom. 18 (2024), no. 3, pp. 953–993

DOI 10.4171/JNCG/545