Equisingularite reelle : invariants locaux et conditions de regularite

TL;DR

This paper introduces new numerical invariants for subanalytic sets that relate curvature and evanescent characteristics, providing insights into their geometry and regularity conditions.

Contribution

It defines two finite sequences of invariants for subanalytic germs, linking curvature and Kashiwara's evanescent characteristics, and studies their properties and continuity.

Findings

Invariants are linear combinations of each other.

Invariants relate to discriminant geometry.

Invariants are continuous along Verdier strata.

Abstract

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 evanescent 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.