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Preprints, Working Papers, ... Year : 2016

THE BV ALGEBRA IN STRING TOPOLOGY OF CLASSIFYING SPACES

Katsuhiko Kuribayashi
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Abstract

For almost any compact connected Lie group $G$ and any field $\mathbb{F}_p$, we compute the Batalin-Vilkovisky algebra $H^{*+\text{dim }G}(LBG;\mathbb{F}_p)$ on the loop cohomology of the classifying space introduced by Chataur and the second author. In particular, if $p$ is odd or $p=0$, this Batalin-Vilkovisky algebra is isomorphic to the Hochschild cohomology $HH^*(H_*(G),H_*(G))$. Over $\mathbb{F}_2$, such isomorphism of Batalin-Vilkovisky algebras does not hold when $G=SO(3)$ or $G=G_2$.
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hal-01380391 , version 1 (13-10-2016)

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Katsuhiko Kuribayashi, Luc Menichi. THE BV ALGEBRA IN STRING TOPOLOGY OF CLASSIFYING SPACES. 2016. ⟨hal-01380391⟩
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