Inequalities defining orbit spaces.
Inner metric properties of 2-dimensional semi-algebraic sets.
We consider 2-dimensional semialgebraic topological manifolds from the differentialgeometric point of view. Curvatures at singularities are defined and a Gauss-Bonnet formula holds. Moreover, Aleksandrov's axioms for an intrinsic geometry of surfaces are fulfilled.
Introduction à la géométrie algébrique réelle
Invariance of domain in o-minimal structures
The aim of this paper is to prove the theorem on invariance of domain in an arbitrary o-minimal structure. We do not make use of the methods of algebraic topology and the proof is based merely on some basic facts about cells and cell decompositions.
Invariance of regularity conditions under definable, locally Lipschitz, weakly bi-Lipschitz mappings
We describe the notion of a weakly Lipschitz mapping on a 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.
Invertible polynomial mappings via Newton non-degeneracy
We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition.