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The bv algebra in string topology of classifying spaces (1610.03970v1)

Published 13 Oct 2016 in math.AT, math.GT, and math.QA

Abstract: For almost any compact connected Lie group $G$ and any field $\mathbb{F}_p$, we compute the Batalin-Vilkoviskyalgebra $H{*+\text{dim }G}(LBG;\mathbb{F}_p)$ 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 $HH(H_(G),H_*(G))$. Over $\mathbb{F}_2$, such isomorphism of Batalin-Vilkovisky algebrasdoes not hold when $G=SO(3)$ or $G=G_2$.

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