Equisingularité réelle II : invariants locaux et conditions de régularité

Georges Comte (1) , Michel Merle (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

For germs of subanalytic sets, we define two finite sequences of new numerical invariants. The first one is obtained by localizing the classical Lipschitz-Killing curvatures, the second one is the real analogue of the vanishing Euler characteristics introduced by M. Kashiwara. We show that each invariant of one sequence is a linear combination of the invariants of the other sequence. We then connect our invariants to the geometry of the discriminants of all dimension. Finally we prove that these invariants are continuous along Verdier strata of a closed subanalytic set.

Mots clés: fibre de Milnor; stratifications de Verdier; courbures de Lipschitz-Killing; densité locale; variétés polaires; ensembles sous-analytiques réels; ensembles analytiques complexes

Domaines: Géométrie métrique [math.MG]; Variables complexes [math.CV]

Georges Comte, Michel Merle. Equisingularité réelle II : invariants locaux et conditions de régularité. Annales Scientifiques de l'École Normale Supérieure, 2008, 41 (2), pp.221-269. ⟨hal-00943624⟩