Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Francesco Bei (Humboldt Universität zu Berlin)
Bott-Chern cohomology groups provide a very important tool in the study of compact complex manifolds. For instance, as recently shown by Angella and Tomassini, Bott-Chern cohomology groups can be used to formulate a purely cohomological criterion that turns out to be equivalent to the validity of the d'd''-lemma.
In this talk we aim to provide an introduction to the basic aspects of the Bott-Chern cohomology and to its connection with the d'd''-lemma. Finally in the last part we will give a brief account on an ongoing project with Paolo Antonini and Sara Azzali whose goal is to extend some aspects of this theory in the setting of Galois coverings and von Neumann dimension.