Volume 19, issue 1 (2019)

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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
Abstract

We construct an equivalence of E2 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