Hochschild homology of finite dimensional algebras.
Rational formality of function spaces.
The cyclic homology of
Sur l'homotopie rationnelle des espaces fonctionnelles.
Homotopie rationnelle et croissance du nombre de géodésiques fermées
Formalité des espaces de lacets libres
The Hochschild cohomology of a closed manifold
Let M be a closed orientable manifold of dimension and be the usual cochain algebra on M with coefficients in a field. The Hochschild cohomology of M, is a graded commutative and associative algebra. The augmentation map induces a morphism of algebras . In this paper we produce a chain model for the morphism I. We show that the kernel of I is a nilpotent ideal and that the image of I is contained in the center of , which is in general quite small. The algebra is expected to be isomorphic...
Rational string topology
We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a simply connected closed manifold . We prove that the loop homology of is isomorphic to the Hochschild cohomology of the cochain algebra with coefficients in . Some explicit computations of the loop product and the string bracket are given.
Page 1