Analytic cell decomposition of sets definable in the structure
We prove that every set definable in the structure can be decomposed into finitely many connected analytic manifolds each of which is also definable in this structure.
Cycles lagrangiens, fonctions constructibles et applications
Finiteness of semialgebraic types of polynomial functions.
Lipschitz stratification of subanalytic sets
Lipschitz stratifications and Lipschitz isotopies
Polytopes secondaires et discriminants
Semi-monotone sets
A coordinate cone in is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of , definable in an o-minimal structure over the reals, such that its intersection with any translation of any coordinate cone is connected. This notion can be viewed as a generalization of convexity. Semi-monotone sets have a number of interesting geometric and combinatorial properties. The main result of the paper is that every semi-monotone...
Stratifications adapted to finite families of differential 1-forms (Pfaffian geometry - Part one).
A first part of a systematic presentation of Pfaffian geometry is given.
Sur la géométrie semi- et sous- analytique
Sur la triangulation des morphismes sous-analytiques
Triangulation of subanalytic sets
Whitney stratification of sets definable in the structure
The aim of this paper is to prove that every subset of definable from addition, multiplication and exponentiation admits a stratification satisfying Whitney’s conditions a) and b).