Batalin-Vilkovisky algebra structures on Hochschild Cohomology

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dc.creatorMenichi, Luc
dc.date2007-11-13
dc.date2007-11-26
dc.date.accessioned2026-07-07T08:44:28Z
dc.date.available2026-07-07T08:44:28Z
dc.descriptionLet $M$ be any compact simply-connected $d$-dimensional smooth manifold and let $\mathbb{F}$ be any field. We show that the Gerstenhaber algebra structure on the Hochschild cohomology on the singular cochains of $M$, $HH^*(S^*(M);S^*(M))$, extends to a Batalin-Vilkovisky algebra. Such Batalin-Vilkovisky algebra was conjecturated to exist and is expected to be isomorphic to the Batalin-Vilkovisky algebra on the free loop space homology on $M$, $H_{*+d}(LM)$ introduced by Chas and Sullivan. We also show that the negative cyclic cohomology $HC^*_-(S^*(M))$ has a Lie bracket. Such Lie bracket is expected to coincide with the Chas-Sullivan string bracket on the equivariant homology $H_*^{S^1}(LM)$.
dc.descriptionminor corrections, essentially typos
dc.identifierhttps://arxiv.org/abs/0711.1946
dc.identifierhttp://arxiv.org/abs/0711.1946
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142663
dc.subjectQuantum Algebra
dc.subjectAlgebraic Topology
dc.titleBatalin-Vilkovisky algebra structures on Hochschild Cohomology
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