et -cohomologies d’une variété compacte privée d’un point. Application à l’intégration sur les cycles
The main purpose of this paper is to present a natural method of decomposition into special cubes and to demonstrate how it makes it possible to efficiently achieve many well-known fundamental results from quasianalytic geometry as, for instance, Gabrielov's complement theorem, o-minimality or quasianalytic cell decomposition.
Applications of singularity theory give rise to many questions concerning deformations of singularities. Unfortunately, satisfactory answers are known only for simple singularities and partially for unimodal ones. The aim of this paper is to give some insight into decompositions of multi-modal singularities with unimodal leading part. We investigate the singularities which have modality k - 1 but the quasihomogeneous part of their normal form only depends on one modulus.
We study deformations of hypersurfaces with one-dimensional singular loci by two different methods. The first method is by using the Le numbers of a hypersurfaces singularity — this falls under the general heading of a “polar” method. The second method is by studying the number of certain special types of singularities which occur in generic deformations of the original hypersurface. We compare and contrast these two methods, and provide a large number of examples.
On donne une condition suffisante explicite et générique pour qu’une forme de Pfaff à deux variables complexes ait ses feuilles denses tant localement que globalement.