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VOL. 82 | 2019 Some differential complexes within and beyond parabolic geometry
Robert L. Bryant, Michael G. Eastwood, A. Rod. Gover, Katharina Neusser

Editor(s) Toshihiro Shoda, Kazuhiro Shibuya

Abstract

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).

Information

Published: 1 January 2019
First available in Project Euclid: 27 November 2019

zbMATH: 07270868

Digital Object Identifier: 10.2969/aspm/08210013

Subjects:
Primary: 53A40, 53D10, 58A12, 58A17, 58J10, 58J70

Rights: Copyright © 2019 Mathematical Society of Japan

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