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-Vilkoviskyalgebra $H^{\ast +\text{dim }G}(LBG;\mathbb{F}\_p)$ on the loop cohomology of the classifying space introduced byChataur and the second author.In particular, if $p$ is odd or $p=0$, this Batalin-Vilkovisky algebra is isomorphicto the Hochschild cohomology $H{H}^{\ast }(H\_\ast (G),H\_\ast (G))$. Over $\mathbb{F}\_2$, such isomorphism of Batalin-Vilkovisky algebrasdoes not hold when $G=SO(3)$ or $G=G\_2$.

References in corpus (2)

• On string topology of classifying spaces
• Higher operations in string topology of classifying spaces

Cited by in corpus (1)

• String topology of finite groups of Lie type