The Batalin–Vilkovisky Algebra in the String Topology of Classifying Spaces
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AbstractFor almost any compact connected Lie group$G$and any field$\mathbb{F}_{p}$, we compute the Batalin–Vilkovisky algebra$H^{\star +\text{dim}\,G}(\text{LBG};\mathbb{F}_{p})$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$HH^{\star }(H_{\star }(G),H_{\star }(G))$. Over$\mathbb{F}_{2}$, such an isomorphism of Batalin–Vilkovisky algebras does not hold when$G=\text{SO}(3)$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.
1995 ◽
Vol 28
(9)
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pp. 2617-2625
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1999 ◽
Vol 14
(08)
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pp. 1225-1259
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1993 ◽
Vol 08
(23)
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pp. 4031-4053
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