On Cohen-Jones isomorphism in string topology
Syunji Moriya

TL;DR
This paper refines the proof of Cohen-Jones isomorphism in string topology by providing detailed geometric modifications and establishing a structured version in symmetric spectra.
Contribution
It offers a detailed correction to the Cohen-Jones proof and extends the isomorphism to a structured setting in symmetric spectra.
Findings
Provides a geometric modification of Cohen-Jones proof
Establishes a structured Cohen-Jones isomorphism in symmetric spectra
Enhances understanding of the loop product and Hochschild cohomology connection
Abstract
The loop product is an operation in string topology. Cohen and Jones gave a homotopy theoretic realization of the loop product as a classical ring spectrum for a manifold . Using this, they presented a proof of the statement that the loop product is isomorphic to the Gerstenhaber cup product on the Hochschild cohomology for simply connected . However, some parts of their proof are technically difficult to justify. The main aim of the present paper is to give detailed modification to a geometric part of their proof. To do so, we set up an "up to higher homotopy" version of McClure-Smith's cosimplicial product. We prove a structured version of Cohen-Jones isomorphism in the category of symmetric spectra.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra
