An isomorphism form intersection homology to Lp-cohomology.
Caractérisation des variétés homologiques à l'aide des invariants d'homologie d'intersection
La conférence de J. P. Brasselet au Symposium de Varsovie a eu pour thème les problèmes actuels de l’homologie d’intersection. Nous en présentons ici l’un des aspects, résultat d’un travail commun réalisé dans le cadre du programme Procope et pendant lequel le second auteur a été chercheur associé au CNRS.
Cheeger-Goreski-MacPherson's conjecture for the varieties with isolated singularities.
Decomposition numbers for perverse sheaves
The purpose of this article is to set foundations for decomposition numbers of perverse sheaves, to give some methods to calculate them in simple cases, and to compute them concretely in two situations: for a simple (Kleinian) surface singularity, and for the closure of the minimal non-trivial nilpotent orbit in a simple Lie algebra.This work has applications to modular representation theory, for Weyl groups using the nilpotent cone of the corresponding semisimple Lie algebra, and for reductive...
Equivariant unfoldings of G-stratified pseudomanifolds.
Intersection cohomology of cs-spaces and Zeeman's filtration.
Intersection cohomology of reductive varieties
We extend the methods developed in our earlier work to algorithmically compute the intersection cohomology Betti numbers of reductive varieties. These form a class of highly symmetric varieties that includes equivariant compactifications of reductive groups. Thereby, we extend a well-known algorithm for toric varieties.
Intersection differential forms
On normal stratified pseudomanifolds.
On the functoriality of stratified desingularizations.
On the geometry of polynomial mappings at infinity
We associate to a given polynomial map from to itself with nonvanishing Jacobian a variety whose homology or intersection homology describes the geometry of singularities at infinity of this map.
Parity sheaves, moment graphs and the -smooth locus of Schubert varieties
We show that the Braden-MacPherson algorithm computes the stalks of parity sheaves. As a consequence we deduce that the Braden-MacPherson algorithm may be used to calculate the characters of tilting modules for algebraic groups and show that the -smooth locus of a (Kac-Moody) Schubert variety coincides with the rationally smooth locus, if the underlying Bruhat graph satisfies a GKM-condition.
Rational BV-algebra in string topology
Let be a 1-connected closed manifold of dimension and be the space of free loops on . M.Chas and D.Sullivan defined a structure of BV-algebra on the singular homology of , . When the ring of coefficients is a field of characteristic zero, we prove that there exists a BV-algebra structure on the Hochschild cohomology which extends the canonical structure of Gerstenhaber algebra. We construct then an isomorphism of BV-algebras between and the shifted homology . We also prove that the...
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.
Regular differential forms on stratified spaces.
Un complexe de formes différentielles à croissance bornée sur une variété stratifiée
Weighted cohomology.
Weights in cohomology and the Eilenberg-Moore spectral sequence
We show that in the category of complex algebraic varieties, the Eilenberg–Moore spectral sequence can be endowed with a weight filtration. This implies that it degenerates if all spaces involved have pure cohomology. As application, we compute the rational cohomology of an algebraic -variety ( being a connected algebraic group) in terms of its equivariant cohomology provided that is pure. This is the case, for example, if is smooth and has only finitely many orbits. We work in the category...