Loop homology algebra of a closed manifold

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The loop homology of a closed orientable manifold M of dimension d is the ordinary homology of the free loop space Mˢ¹ with degrees shifted by d, i.e. H*(Mˢ¹) = H*₊d(Mˢ¹). Chas and Sullivan have defined a loop product on H*(Mˢ¹) and an intersection morphism I: H*(Mˢ¹) → H*(ΩM). The algebra H*(Mˢ¹) is commutative and I is a morphism of algebras. In this paper we produce a model that computes the algebra H*(Mˢ¹) 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.