E2 structures and derived Koszul duality in string topology

Blumberg, Andrew; Mandell, Michael

doi:10.2140/agt.2019.19.239

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$E_2$ structures and derived Koszul duality in string topology

Andrew J Blumberg and Michael A Mandell

Algebraic & Geometric Topology 19 (2019) 239–279

DOI: 10.2140/agt.2019.19.239

Abstract

We construct an equivalence of $E_{2}$ algebras between two models for the Thom spectrum of the free loop space that are related by derived Koszul duality. To do this, we describe the functoriality and invariance properties of topological Hochschild cohomology.

Keywords

topological Hochschild cohomology, string topology, derived Koszul duality, $E_2$ algebra, centralizer condition

Mathematical Subject Classification 2010

Primary: 55P50

Secondary: 16D90, 16E40

References

Publication

Received: 12 January 2018

Revised: 8 August 2018

Accepted: 25 September 2018

Published: 6 February 2019

Authors

Andrew J Blumberg
Department of Mathematics The University of Texas Austin, TX United States

Michael A Mandell
Department of Mathematics Indiana University Bloomington, IN United States

Volume 19, issue 1 (2019)