# THE BV ALGEBRA IN STRING TOPOLOGY OF CLASSIFYING SPACES

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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Cited literature [38 references]

https://hal.archives-ouvertes.fr/hal-01380391
Contributor : Luc Menichi <>
Submitted on : Thursday, October 13, 2016 - 8:48:52 AM
Last modification on : Monday, March 9, 2020 - 6:15:53 PM
Document(s) archivé(s) le : Saturday, February 4, 2017 - 8:53:32 PM

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loop_coproducts_onBG10.pdf
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### Identifiers

• HAL Id : hal-01380391, version 1
• ARXIV : 1610.03970

### Citation

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

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