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arXiv · 2003.03704

On Cohen-Jones isomorphism in string topology

Syunji Moriya
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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 $LM^{-TM}$ for a manifold $M$. Using this, they presented a proof of the statement that the loop product is isomorphic to the Gerstenhaber cup product on the Hochschild cohomology $HH^*(C^*(M)\,;C^*(M))$ for simply connected $M$. 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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Syunji Moriya. 2020-03-08. On Cohen-Jones isomorphism in string topology. https://arxiv.org/abs/2003.03704

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