Rational BV-algebra in String Topology
| dc.creator | Felix, Yves | |
| dc.creator | Thomas, Jean-Claude | |
| dc.date | 2007-05-29 | |
| dc.date.accessioned | 2026-07-07T08:03:29Z | |
| dc.date.available | 2026-07-07T08:03:29Z | |
| dc.description | Let $M$ 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.identifier | https://arxiv.org/abs/0705.4194 | |
| dc.identifier | http://arxiv.org/abs/0705.4194 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129597 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 55P35-54N45-55N33-17A65-81T30-17B55 | |
| dc.title | Rational BV-algebra in String Topology | |
| dc.type | text |