A Decomposition Theorem for the Integral Homology of a Variety.
Arrangements and Milnor fibres.
Bernstein-Gelfand-Gelfand reciprocity on perverse sheaves
Bi-Lipschitz trivialization of the distance function to a stratum of a stratification
Given a Lipschitz stratification 𝒳 that additionally satisfies condition (δ) of Bekka-Trotman (for instance any Lipschitz stratification of a subanalytic set), we show that for every stratum N of 𝒳 the distance function to N is locally bi-Lipschitz trivial along N. The trivialization is obtained by integration of a Lipschitz vector field.
Classes caractéristiques et théorèmes d'indice : point de vue microlocal
Conditions de régularité et éclatements
On décrit trois types de conditions permettant de stratifier un morphisme analytique complexe :1) différentielles, à la Thom-Whitney,2) géométriques, demandant l’équidimensionnalité de certains diviseurs exceptionnels obtenus à partir de l’espace conormal relatif ou de la modification de Nash relative de ,3) numériques, exigeant la constance d’invariants de le long des states.On donne une méthode générale permettant d’exprimer et de démontrer des équivalences entre des conditions de chaque...
Conditions de Whitney et sections planes.
Ein Beitrag zur Whitney-Regularität im unendlichdimensionalen Fall.
Elementary construction of perverse sheaves.
Équisingularité réelle : nombres de Lelong et images polaires
Explicit models for perserse sheaves.
We consider categories of generalized perverse sheaves, with relaxed constructibility conditions, by means of the process of gluing t-structures and we exhibit explicit abelian categories defined in terms of standard sheaves categories which are equivalent to the former ones. In particular , we are able to realize perverse sheaves categories as non full abelian subcategories of the usual bounded complexes of sheaves categories. Our methods use induction on perversities. In this paper, we restrict...
Faisceaux pervers dont le support singulier est une courbe plane
Harmonic metrics and connections with irregular singularities
We identify the holomorphic de Rham complex of the minimal extension of a meromorphic vector bundle with connexion on a compact Riemann surface with the complex relative to a suitable metric on the bundle and a complete metric on the punctured Riemann surface. Applying results of C. Simpson, we show the existence of a harmonic metric on this vector bundle, giving the same complex.
Inégalités d'auto-intersection pour les courants positifs fermés définis dans les variétés projectives
Intégration de classes de cohomologie méromorphes et diviseurs d'incidence
Intersection Homology II.
Invariance of regularity conditions under definable, locally Lipschitz, weakly bi-Lipschitz mappings
We describe the notion of a weakly Lipschitz mapping on a stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the Verdier condition.
L2-Cohomologie des espaces stratifiés.
Lefschetz fixed point theorem for intersection homology.