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.