Institut de Mathématiques de Marseille, UMR 7373


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On the local geometry of definably stratified sets

Jeudi 16 février 14:00-15:00 - David TROTMAN - I2M, Aix-Marseille Université

On the local geometry of definably stratified sets

Résumé : With Guillaume Valette (IMPAN, Cracovie).
We prove that a 1985 theorem of Pawlucki, showing that Whitney regularity for a subanalytic set S with a smooth singular locus of codimension one implies that S is a finite union of C1 manifolds with boundary, applies to definable sets in polynomially bounded o-minimal structures. We give a refined version of Pawlucki’s theorem for arbitrary o-minimal structures, replacing Whitney (b)-regularity by a quantified version, and prove related results concerning normal cones and continuity of the density. We analyse two counterexamples to the extension of Pawlucki’s theorem to definable subsets in general o-minimal structures, and to several other statements valid for subanalytic sets.
In particular we give the first example of a Whitney (b)-regular definably stratified set for which the density is not continuous along a stratum.

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