Some differential complexes within and beyond parabolic geometry

Details Some differential complexes within and beyond parabolic geometry Some differential complexes within and beyond parabolic geometry

2011-12-09

arxiv.org/abs/1112.2142v3

Mathematics

Differential Geometry

28 pages. An oversight pointed out to us by Boris Doubrov has been corrected and other minor modifications made

Scientific paper

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.

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