On the basic Dolbeault cohomology of Sasakian manifolds 

Oliver Goertsches (Marburg)

Abstract: In this talk, which is based on joint work with Hiraku Nozawa and Dirk Toeben, 
we will illustrate a few properties of the basic Dolbeault cohomology of compact Sasakian 
manifolds. In contrast to ordinary basic cohomology this interesting invariant can distinguish 
different Sasakian structures on the same smooth manifold. Among other things, we will 
explain that it indeed only depends on the underlying CR structure, as well as a 
Carrell-Lieberman type localization theorem that relates the basic Hodge numbers 
to those of the union of closed Reeb orbits.