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Bi-Lipschitz trivialization of the distance function to a stratum of a stratification

Adam Parusiński (2005)

Annales Polonici Mathematici

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.

Conditions de régularité et éclatements

Jean-Pierre Henry, Michel Merle (1987)

Annales de l'institut Fourier

On décrit trois types de conditions permettant de stratifier un morphisme analytique complexe f  :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 f ,3) numériques, exigeant la constance d’invariants de f le long des states.On donne une méthode générale permettant d’exprimer et de démontrer des équivalences entre des conditions de chaque...

Explicit models for perserse sheaves.

Félix Gudiel Rodríguez, Luis Narváez Macarro (2003)

Revista Matemática Iberoamericana

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...

Harmonic metrics and connections with irregular singularities

Claude Sabbah (1999)

Annales de l'institut Fourier

We identify the holomorphic de Rham complex of the minimal extension of a meromorphic vector bundle with connexion on a compact Riemann surface X with the L 2 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 L 2 complex.

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