december 2023 A note on the string topology BV-algebra for $S^2$ with ${\mathbb Z}_2$ coefficients
Kate Poirier, Thomas Tradler
Bull. Belg. Math. Soc. Simon Stevin 30(4): 482-509 (december 2023). DOI: 10.36045/j.bbms.230322

Abstract

Luc Menichi showed that the BV algebras on $H_\bullet(L S^2;{\mathbb Z}_2)[-2]$ coming from string topology and the one on $HH^\bullet(H^\bullet( S^2;{\mathbb Z}_2), H^\bullet( S^2;{\mathbb Z}_2))$ using Poincaré duality on $H^\bullet( S^2;{\mathbb Z}_2)$ are not isomorphic. In this note we show how one can obtain the string topology BV algebra on Hochschild cohomology using a Poincaré duality structure with higher homotopies. This Poincaré duality (with higher homotopies) on cohomology is induced by a local Poincaré duality (with higher homotopies) on the cochain level.

Citation

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Kate Poirier. Thomas Tradler. "A note on the string topology BV-algebra for $S^2$ with ${\mathbb Z}_2$ coefficients." Bull. Belg. Math. Soc. Simon Stevin 30 (4) 482 - 509, december 2023. https://doi.org/10.36045/j.bbms.230322

Information

Published: december 2023
First available in Project Euclid: 31 December 2023

Digital Object Identifier: 10.36045/j.bbms.230322

Subjects:
Primary: 16E40 , 55P50
Secondary: 08A65 , 57P10

Keywords: BV algebra , Hochschild cohomology , Poincaré duality , string topology

Rights: Copyright © 2023 The Belgian Mathematical Society

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Vol.30 • No. 4 • december 2023
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