Micheline Vigué-Poirrier

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 1-connected closed manifold

Cyclic homology of algebraic hypersurfaces

M

Two classes of algebras with infinite Hochschild homology

. We prove that the loop homology of

Free loop spaces of finite complexes have infinite category

M

Hochschild homology criteria for trivial algebra structures

is isomorphic to the Hochschild cohomology of the cochain algebra

Hochschild and cyclic homology of an almost commutative cochain algebra associated to a nilmanifold

C^\ast(M)

Dihedral homology of commutative algebras

with coefficients in itself. Some explicit computations of the loop product and the string bracket are given.

The Hochschild cohomology of a closed manifold

Abstract A formula is given for the cyclic homology of commutative algebras of the form k[x 1 ,…,x,] (P) with P a weighted homogenous polynomial. For r⩽3, we have explicit results: HC2n(k[x1+x2]/(P)) = k for n > 0, HC 2n+1 ( k[x 1 ,…,x,] (P) ) ∽ k[x 1 , x 2 ] ∂P ∂x 1 , ∂P ∂x 2 if P is irreducible; HC 2n+1 (k[x 1 , x 2 , x 3 ] (P) ) = 0 and HC 2n (k[x 1 , x 2 , x 3 ] (P) ) ∽ k ⊗ k[x 1 , x 2 , x 3 ] ∂P ∂x 1 , ∂P ∂x 2 , ∂P ∂x 3 for n>0 if P is irreducible and has only an isolated singularity at the origin.

The rational homotopy theory of certain path spaces with applications to geodesics

We prove without any assumption on the ground field that higher Hochschild homology groups do not vanish for two large classes of algebras whose global dimension is not finite.

Réalisation de morphismes donnés en cohomologie et suite spectrale d’Eilenberg-Moore

Let X be a 1-connected space such that each H(j)(X;Z) is finitely generated. In this paper we prove that if the reduced homology of X with coefficients in a field is nonzero, then the Lusternik-Schnirelmann category of the free loop space is infinite.