Multiplicity Mod 2 as a Semi-algebraic Bi-lipschitz Invariant
نویسنده
چکیده
We study the multiplicity mod 2 of real algebraic hypersurfaces. We prove that under some assumptions on the singularity it is preserved through a semi-algebraic bi-Lipschitz homeomorphism of R. In a first part we find a part of the tangent cone enclosing the multiplicity mod 2 and prove that it is an equivariant subset of S. Studying equivariant submanifolds of S we are able to conclude about its invariance through semi-algebraic bi-Lipschitz homeomorphisms whenever the tangent cone has an isolated singularity at the origin.
منابع مشابه
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 R. 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 is preserved by the antipodal map. The stud...
متن کامل2 00 9 Invariance of Regularity Conditions under Definable , Locally Lipschitz , Weakly Bi - Lipschitz Mappings
In this paper we describe the notion of a weak lipschitzianity of a mapping on a C stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the Verdier condition.
متن کاملBi-Lipschitz Mappings and Quasinearly Subharmonic Functions
After considering a variant of the generalized mean value inequality of quasinearly subharmonic functions, we consider certain invariance properties of quasinearly subharmonic functions. Kojić has shown that in the plane case both the class of quasinearly subharmonic functions and the class of regularly oscillating functions are invariant under conformal mappings. We give partial generalization...
متن کاملInvariants of Bi-lipschitz Equivalence of Real Analytic Functions
We construct an invariant of the bi-Lipschitz equivalence of analytic function germs (Rn,0) → (R,0) that varies continuously in many analytic families. This shows that the bi-Lipschitz equivalence of analytic function germs admit continuous moduli. For a germ f the invariant is given in terms of the leading coefficients of the asymptotic expansions of f along the sets where the size of |x||grad...
متن کاملParameterized Cache Coherence Protocol Verification using Invariant
Verification of parameterized cache coherence protocol is very important in the share-memory multiprocessor system. In this paper, a new method was proposed to verify the correctness of parameterized cache coherence protocol based on the invariant. Firstly, we present the parameterized cache coherence protocol as semi-algebraic transition system, and then solve the invariant of transition syste...
متن کامل