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

Kate Poirier; Thomas Tradler

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

Algebraic Topology 2023-01-16 v1

Authors: Kate Poirier , Thomas Tradler

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.

Keywords

string topology BV algebra Hochschild cohomology Poincaré duality higher homotopies

Cite

@article{arxiv.2301.05381,
  title  = {A note on the string topology BV-algebra for $S^2$ with $Z_2$ coefficients},
  author = {Kate Poirier and Thomas Tradler},
  journal= {arXiv preprint arXiv:2301.05381},
  year   = {2023}
}

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22 pages

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

Abstract

Keywords

Cite

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