Multiplicity mod 2 as a Metric Invariant

We study the multiplicity modulo 2 of real analytic hypersurfaces. We prove that, under some assumptions on the singularity, the multiplicity modulo 2 is preserved by subanalytic bi-Lipschitz homeomorphisms of Rn . In the first part of the paper, we find a subset of the tangent cone which determines the multiplicity mod 2 and prove that this subset of Sn is preserved by the antipodal map. The study of such subsets of Sn enables us to deduce the subanalytic metric invariance of the multiplicity modulo 2 under some extra assumptions on the tangent cone. We also prove a real version of a theorem of Comte, and yield that the multiplicity modulo 2 is preserved by arc-analytic bi-Lipschitz homeomorphisms.

• Type: Journal
• Year: 2010
• Where: DCG
• Authors: Guillaume Valette
• Keywords: Bi-Lipschitz Homeomorphisms, DCG 2010, Multiplicity Modulo, Tangent Cone