Volume 21, issue 7 (2021)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 22
Issue 5, 2007–2532
Issue 4, 1497–2006
Issue 3, 991–1495
Issue 2, 473–990
Issue 1, 1–472

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
The Hochschild complex of a finite tensor category

Christoph Schweigert and Lukas Woike

Algebraic & Geometric Topology 21 (2021) 3689–3734
Abstract

Modular functors, ie consistent systems of projective representations of mapping class groups of surfaces, were constructed for nonsemisimple modular categories decades ago. Concepts from homological algebra have not been used in this construction although it is an obvious question how they should enter in the nonsemisimple case. We elucidate the interplay between the structures from topological field theory and from homological algebra by constructing a homotopy coherent projective action of the mapping class group SL(2, ) of the torus on the Hochschild complex of a modular category. This is a further step towards understanding the Hochschild complex of a modular category as a differential graded conformal block for the torus. Moreover, we describe a differential graded version of the Verlinde algebra.

Keywords
modular functor, Hochschild complex, finite tensor category, mapping class group
Mathematical Subject Classification
Primary: 13D03, 18M15, 57K16
References
Publication
Received: 4 October 2020
Revised: 7 January 2021
Accepted: 30 January 2021
Published: 28 December 2021
Authors
Christoph Schweigert
Fachbereich Mathematik
Universität Hamburg
Hamburg
Germany
Lukas Woike
Institut for Matematiske Fag
Københavns Universitet
København
Denmark