Multiplicity mod 2 as a Metric Invariant

作者：Valette Guillaume^*

来源：Discrete & Computational Geometry, 2010, 43(3): 663-679.

DOI：10.1007/s00454-009-9205-z

• Real analytic hypersurfaces
• Multiplicity
• 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 a"e (n) . 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 S (n) is preserved by the antipodal map. The study of such subsets of S (n) 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.

• 出版日期2010-4