2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63564The 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.New version 19 pagesAlgebraic Topology55P35, 54N45,55N33, 17A65, 81T30, 17B55text