Loop homology algebra of a closed manifold
| dc.creator | Félix, Yves | |
| dc.creator | Thomas, Jean-Claude | |
| dc.creator | Vigué-Poirrier, Micheline | |
| dc.date | 2002-03-14 | |
| dc.date | 2003-06-27 | |
| dc.date.accessioned | 2026-07-07T04:47:03Z | |
| dc.date.available | 2026-07-07T04:47:03Z | |
| dc.description | The loop homology of a closed orientable manifold $M$ of dimension $d$ is the ordinary homology of the free loop space $M^{S^1}$ with degrees shifted by $d$, i.e. $\mathbb H_*(M^{S^1}) = H_{*+d}(M^{S^1})$. Chas and Sullivan have defined a loop product on $\mathbb H_*(M^{S^1})$ and an intersection morphism $I : \mathbb H_*(M^{S^1}) \to H_*(ΩM)$. The algebra $\mathbb H_*(M^{S^1})$ is commutative and $I$ is a morphism of algebras. In this paper we produce a model that computes the algebra $\mathbb H_*(M^{S^1})$ and the morphism $I$. We show that the kernel of $I$ is nilpotent and that the image is contained in the center of $H_*(ΩM)$, which is in general quite small. | |
| dc.description | New version 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0203137 | |
| dc.identifier | http://arxiv.org/abs/math/0203137 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63564 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55P35, 54N45,55N33, 17A65, 81T30, 17B55 | |
| dc.title | Loop homology algebra of a closed manifold | |
| dc.type | text |