On (w) and (ts)-regular stratifications.
Perfect stratifications and theory of weights.
In this paper we emphasize Deligne's theory of weights, in order to prove that some stratifications of algebraic varieties are perfect. In particular, we study in some detail the Bialynicki-Birula's stratifications and the stratifications considered by F. Kirwan to compute the cohomology of symplectic or geometric quotients. Finally we also appoint the motivic formulation of this approach, which contains the Hodge theoretic formulation.
Quelques notions d’espaces stratifiés
Real algebraic structures on topological spaces
Scalar curvature of defineable CAT-spaces.
Smoothness and geometry of boundaries associated to skeletal structures I: sufficient conditions for smoothness
We introduce a skeletal structure in , which is an - dimensional Whitney stratified set on which is defined a multivalued “radial vector field” . This is an extension of notion of the Blum medial axis of a region in with generic smooth boundary. For such a skeletal structure there is defined an “associated boundary” . We introduce geometric invariants of the radial vector field on and a “radial flow” from to . Together these allow us to provide sufficient numerical conditions for...
Stratifications of polynomial spaces
In the paper we construct some stratifications of the space of monic polynomials in real and complex cases. These stratifications depend on properties of roots of the polynomials on some given semialgebraic subset of R or C. We prove differential triviality of these stratifications. In the real case the proof is based on properties of the action of the group of interval exchange transformations on the set of all monic polynomials of some given degree. Finally we compare stratifications corresponding...
Stratifications of teardrops
Teardrops are generalizations of open mapping cylinders. We prove that the teardrop of a stratified approximate fibration X → Y × ℝ with X and Y homotopically stratified spaces is itself a homotopically stratified space (under mild hypothesis). This is applied to manifold stratified approximate fibrations between manifold stratified spaces in order to establish the realization part of a previously announced tubular neighborhood theory.
Stratifikation von Quotientenmannigfaltigkeiten (in Charakteristik 0) und insbesondere der Modulmannigfaltigkeiten für Kurven.
Sur la condition de Thom stricte pour un morphisme analytique complexe
Topological classification of multiaxial -actions (with an appendix by Jared Bass)
This paper begins the classification of topological actions on manifolds by compact, connected, Lie groups beyond the circle group. It treats multiaxial topological actions of unitary and symplectic groups without the dimension restrictions used in earlier works by M. Davis and W. C. Hsiang on differentiable actions. The general results are applied to give detailed calculations for topological actions homotopically modeled on standard multiaxial representation spheres. In the present topological...
Triangulations of 3-dimensional pseudomanifolds with an application to state-sum invariants.
Volume and multiplicities of real analytic sets
We give criteria of finite determinacy for the volume and multiplicities. Given an analytic set described by {v = 0}, we prove that the log-analytic expansion of the volume of the intersection of the set and a "little ball" is determined by that of the set defined by the Taylor expansion of v up to a certain order if the mapping v has an isolated singularity at the origin. We also compare the cardinalities of finite fibers of projections restricted to such a set.
Whitney regularity and generic wings
Given adjacent subanalytic strata in verifying Kuo’s ratio test (resp. Verdier’s -regularity) we find an open dense subset of the codimension submanifolds (wings) containing such that is generically Whitney -regular is exactly one more than the dimension...