Subcomplexes in curved Bernstein-Gelfand-Gelfand sequences

Andreas Cap
(University of Vienna)

Abstract: Curved BGG sequences are not complexes in general. In my lecture, I will discuss recent joint work with V. Soucek (Prague) which shows that for certain geometric structure and under appropriate assumptions on torsion freeness and/or semiflatness, there is a conceptual way to identify parts of BGG sequences as complexes. This applies for example to CR structures of hypersurface type and to quaternionic structures. In the latter case, one obtains elliptic complexes in many cases. In particular, we construct an elliptic deformation comples for quaternionic structures.