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arXiv · 2301.05381

A note on the string topology BV-algebra for $S^2$ with $Z_2$ coefficients

Kate Poirier·Thomas Tradler
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Abstract

Luc Menichi showed that the BV algebras on $H^\bullet(LS^2;Z_2)[-2]$ coming from string topology and the one on $HH^\bullet(H^\bullet(S^2;Z_2),H^\bullet(S^2;Z_2))$ using Poincar\'e duality on $H^\bullet(S^2;Z_2)$ are not isomorphic. In this note we show how one can obtain the string topology BV algebra on Hochschild cohomology using a Poincar\'e duality structure with higher homotopies. This Poincar\'e duality (with higher homotopies) on cohomology is induced by a local Poincar\'e duality (with higher homotopies) on the cochain level.

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Kate Poirier, Thomas Tradler. 2023-01-13. A note on the string topology BV-algebra for $S^2$ with $Z_2$ coefficients. https://arxiv.org/abs/2301.05381

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