Homology, Homotopy and Applications

Volume 22 (2020)

Number 1

Equivariant higher Hochschild homology and topological field theories

Pages: 27 – 54

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n1.a3


Lukas Müller (Department of Mathematics, Heriot-Watt University, Edinburgh, Scotland, United Kingdom)

Lukas Woike (Fachbereich Mathematik, Bereich Algebra und Zahlentheorie, Universität Hamburg, Germany)


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.


Hochschild homology, topological field theory, bordism category, principal bundle, $E_{\infty}$-algebra

2010 Mathematics Subject Classification

13D03, 81T45

Copyright © 2019 Lukas Müller and Lukas Woike. Permission to copy for private use granted.

L.M. is supported by the Doctoral Training Grant ST/N509099/1 from the UK Science and Technology Facilities Council (STFC). L.W. is supported by the RTG 1670 “Mathematics inspired by String theory and Quantum Field Theory” and thanks the Heriot-Watt University in Edinburgh and, in particular, Richard Szabo for their hospitality during the time when part of this project was completed.

Received 9 October 2018

Received revised 6 May 2019

Accepted 7 May 2019

Published 18 September 2019