THE BV ALGEBRA IN STRING TOPOLOGY OF CLASSIFYING SPACES

Katsuhiko Kuribayashi (1) , Luc Menichi (2)

1 Shinshu University, Matsumoto
2 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

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 $G=G_2$.

Mots clés: String topology; Batalin-Vilkovisky algebra; Classifying space.

Domaines: Topologie algébrique [math.AT]; Topologie géométrique [math.GT]; Algèbres quantiques [math.QA]

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