Equisingularite reelle : invariants locaux et conditions de regularite

Details Equisingularite reelle : invariants locaux et conditions de regularite Equisingularite reelle : invariants locaux et conditions de regularite

2007-06-27

arxiv.org/abs/0706.4061v3

Ann. Sci. \'Ecole Norm. Sup., s\'erie 4, 41, fascicule 2 (2008), 221-269

Mathematics

Differential Geometry

49 pages, 1 figure

Scientific paper

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.

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