Families of functions on analytic varieties

Quand

10 novembre 2011    
The Milnor number plays a fundamental rôle in the classification of complex hypersurface singularities and in equisingularity problems of families of functions with isolated singularities. The celebrated Lê-Ramanujan’s theorem says that $\mu$-constant deformations of isolated hypersurface singularities are topologically trivial. The characterization of the topological triviality in the case of families of functions with isolated singularities defined on an analytic variety $V$ is still an open problem. Bruce and Roberts introduce a generalization of the Milnor number of $f,$ which we call Bruce-Roberts number, $ \mu_{BR}(V,f)$. Like the Milnor number of $f$ , this number shows properties of $f$ and $V.$ The aim of this talk is to discuss properties of this invariant and its rôle in the study of functions on analytic varieties.