Lê cycles and Milnor classes.

Carte non disponible

Date(s) - 7 février 2013

Catégories Pas de Catégories

The Lê cycles are analytic cycles that describe the diffeomorphism type of the Milnor fibre of holomorphic map-germs. Given a codimension one analytic subvariety Z of a compact complex manifold M, one has global Lê cycles, obtained by “gluing” the local Lê cycles. The Milnor classes of Z are defined as the difference between its Schwartz-McPherson and its Fulton-Johnson classes, both of these being extensions to compact singular varieties of the classical Chern classes of complex manifolds. I will speak about joint work with R. Callejas-Bedregal and M. Morgado, expressing the Milnor classes in terms of the Lê cycles and viceversa. This shows that the information encoded in the Mlnor classes of Z essentially determine the topology of the local Milnor fibres of Z, and the geometry of the local Milnor fibres determines the global Milnor classes.