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The Batalin-Vilkovisky Algebra in the String Topology of Classifying Spaces

Kuribayashi, Katsuhiko Menichi, Luc 信州大学 DOI:10.4153/CJM-2018-021-9

2021.02.22

概要

For almost any compact connected Lie group C and any field F-p, we compute the Batalin-Vilkovisky algebra H*(+dim G) (LBG; 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 F-2, such an isomorphism of Batalin-Vilkovisky algebras does not hold when G = SO(3) or G = G(2). Our elaborate considerations on the signs in string topology of the classifying spaces give rise to a general theorem on graded homological conformal field theory.

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...

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