Equivariant Higher Hochschild Homology and Topological Field Theories

TL;DR

This paper develops an equivariant version of higher Hochschild homology for spaces with principal G-bundles, extending it to an equivariant topological field theory valued in cospans of E-infinity algebras.

Contribution

It introduces a new equivariant Hochschild homology theory for G-spaces with principal bundles and constructs an associated equivariant topological field theory.

Findings

Established an equivariant excision property.

Extended the theory to an equivariant topological field theory.

Valued the theory in the $( abla,1)$-category of cospans of E-infinity algebras.

Abstract

We present a version of higher Hochschild homology for spaces equipped with principal bundles for a structure group $G$. As coefficients, we allow $E_\infty$-algebras with $G$-action. For this homology theory, we establish an equivariant version of excision and prove that it extends to an equivariant topological field theory with values in the $(\infty,1)$-category of cospans of $E_\infty$-algebras.