Some differential complexes within and beyond parabolic geometry

Journal Article (Academic article)

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.

Full Text

Duke Authors

Cited Authors

  • Bryant, RL; Eastwood, MG; Gover, AR; Neusser, K

Published Date

  • November 22, 2019

Published In

  • Advanced Studies in Pure Mathematics

Volume / Issue

  • 82 / Differential Geometry and Tanaka Theory

Start / End Page

  • 13 - 40

Published By


  • 29