Thuy Nguyen: Characteristic classes of analytic complex varieties

V torek, 15. oktobra ob 12. uri in 30 minut, bo v okviru seminarja za kompleksno analizo predavala dr. Thuy Nguyen z univerze Sao Paulo State University, Brazilija.

Title: Characteristic classes of analytic complex varieties.

Abstract: For a long time, it was unknown if it is possible to construct characteristic classes in the case of singular varieties. The real case has been solved by Sullivan-Wu. In the complex case, in 1965 Marie-Helene Schwartz gave a construction of characteristic classes, by obstruction theory, in the framework of Whitney stratifications. Her first idea is to consider the dual cell decomposition, dual to a triangulation compatible with the stratification. That allows us to construct a cocycle with the right dimension on each stratum. The second idea of M.-H. Schwartz, which is very nice and beautiful, is to consider stratified frames, obtained by suitable radial extensions so that the resulting class does not depend on the considered frame. The M.-H. Schwartz’s proof is rather difficult. It uses complicated and delicate constructions of systems of adapted tubular neighborhoods. Moreover, it needs to consider technical homotopies between frames. In this talk we will first give an introduction or at least the idea of the Schwartz's construction above-mentioned. After, we will present how to use Lipschitz stratifications, instead of Whitney stratifications, to simplify this construction. In particular, a proof of the Poincare-Hopf Theorem for singular varieties using Lipschitz stratifications will be also presented as a consequence of this study. (Joint-work with Jean-Paul Brasselet and Tadeusz Mostowski)

Predavanje bo potekalo hibridno, v predavalnici 3.05 na Jadranski 21 in preko aplikacije ZOOM:

https://uni-lj-si.zoom.us/j/99382527395

Meeting ID: 993 8252 7395

Vljudno vabljeni!

Vodji seminarja

Franc Forstneric in Barbara Drinovec Drnovsek