Some differential complexes within and beyond parabolic geometry
| Autor: | A. Rod Gover, Michael Eastwood, Robert L. Bryant, Katharina Neusser |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Mathematics - Differential Geometry
53A40 53D10 58A12 58A17 58J10 58J70 Pure mathematics 58J70 58A12 53A40 Structure (category theory) 58A17 01 natural sciences Bernstein-Gelfand-Gelfand complex 58J10 Parabolic geometry Simple (abstract algebra) 0103 physical sciences FOS: Mathematics Trivial representation 0101 mathematics Physics 010102 general mathematics Rumin complex 53D10 Differential Geometry (math.DG) Differential complexes Sheaf 010307 mathematical physics Constant function Differential (mathematics) Symplectic geometry |
| Zdroj: | Differential Geometry and Tanaka Theory — Differential System and Hypersurface Theory —, T. Shoda and K. Shibuya, eds. (Tokyo: Mathematical Society of Japan, 2019) |
| ISSN: | 0920-1971 |
| DOI: | 10.2969/aspm/08210013 |
| Popis: | 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 certain geometries beyond the parabolic realm. 28 pages. An oversight pointed out to us by Boris Doubrov has been corrected and other minor modifications made |
| Databáze: | OpenAIRE |
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