$E_{2}$ Structures and Derived Koszul Duality in String Topology

TL;DR

This paper establishes an equivalence of $E_{2}$ algebra structures between two models of the Thom spectrum of free loop spaces, using derived Koszul duality and analyzing topological Hochschild cohomology.

Contribution

It introduces a new equivalence of $E_{2}$ algebra models for Thom spectra related by derived Koszul duality, expanding understanding of string topology structures.

Findings

Demonstrates an $E_{2}$ algebra equivalence between models of Thom spectra

Describes functoriality and invariance of topological Hochschild cohomology

Connects derived Koszul duality with string topology

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.