Publication details
Some differential complexes within and beyond parabolic geometry
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Proceedings |
| Conference | Differential Geometry and Tanaka Theory - Differential System and Hypersurface Theory |
| MU Faculty or unit | |
| Citation | |
| Web | https://projecteuclid.org/euclid.aspm/1574872398 |
| Doi | http://dx.doi.org/10.2969/aspm/08210013 |
| Keywords | Differential complexes; Rumin complex; Parabolic geometry; Bernstein-Gelfand-Gelfand complex |
| Description | For smooth manifolds equipped with various geometric structures, we construct complexes that replace the de Rham complex in providing an alternative fine resolution of the sheaf of locally constant functions. In case that the geometric structure is that of a parabolic geometry, our complexes coincide with the Bernstein-Gelfand-Gelfand complex associated with the trivial representation. However, at least in the cases we discuss, our constructions are relatively simple and avoid most of the machinery of parabolic geometry. Moreover, our method extends to contact and symplectic geometries (beyond the parabolic realm). |