Rational BV-algebra in String Topology

dc.creatorFelix, Yves
dc.creatorThomas, Jean-Claude
dc.date2007-05-29
dc.date.accessioned2026-07-07T08:03:29Z
dc.date.available2026-07-07T08:03:29Z
dc.descriptionLet $M$ be a 1-connected closed manifold and $LM$ be the space of free loops on $M$. In \cite{C-S} M. Chas and D. Sullivan defined a structure of BV-algebra on the singular homology of $LM$, $H_\ast(LM; \bk)$. When the field of coefficients is of characteristic zero, we prove that there exists a BV-algebra structure on $\hH^\ast(C^\ast (M); C^\ast (M))$ which carries the canonical structure of Gerstenhaber algebra. We construct then an isomorphism of BV-algebras between $\hH^\ast (C^\ast (M); C^\ast (M)) $ and the shifted $ H_{\ast+m} (LM; {\bk})$. We also prove that the Chas-Sullivan product and the BV-operator behave well with the Hodge decomposition of $H_\ast (LM) $.
dc.identifierhttps://arxiv.org/abs/0705.4194
dc.identifierhttp://arxiv.org/abs/0705.4194
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/129597
dc.subjectAlgebraic Topology
dc.subjectClassical Analysis and ODEs
dc.subject55P35-54N45-55N33-17A65-81T30-17B55
dc.titleRational BV-algebra in String Topology
dc.typetext

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