6 nov 2018 -- 16:00
Aula D'Antoni, Dip.Matematica, Università "Tor Vergata", Roma
Abstract.
The Cech-de Rham cohomology together with its integration theory has been effectively used in various problems related to localization of characteristic classes. Likewise we may develop the Cech-Dolbeault cohomology theory and on the way we naturally come up with the relative Dolbeault cohomology.
This cohomology turns out to be canonically isomorphic with the local (relative) cohomology of A. Grothendieck and M. Sato so that it provides a handy way of representing the latter.
In this talk we present the theory of relative Dolbeault cohomology and give, as applications, simple explicit expressions of Sato hyperfunctions, some fundamental operations on them and related local duality theorems. Particularly noteworthy is that the integration of hyperfunctions in our framework, which is a descendant of the integration theory on the ¥v{C}echech-de Rham cohomology, is simply given as the usual integration of Stokes type. Also the Thom class in relative de Rham cohomology plays an essential role in the scene of interaction between topology and analysis.
The talk includes a joint work with N. Honda and T. Izawa.