Loop homology algebra of a closed manifold

dc.creatorFélix, Yves
dc.creatorThomas, Jean-Claude
dc.creatorVigué-Poirrier, Micheline
dc.date2002-03-14
dc.date2003-06-27
dc.date.accessioned2026-07-07T04:47:03Z
dc.date.available2026-07-07T04:47:03Z
dc.descriptionThe 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.descriptionNew version 19 pages
dc.identifierhttps://arxiv.org/abs/math/0203137
dc.identifierhttp://arxiv.org/abs/math/0203137
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63564
dc.subjectAlgebraic Topology
dc.subject55P35, 54N45,55N33, 17A65, 81T30, 17B55
dc.titleLoop homology algebra of a closed manifold
dc.typetext

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