Differential invariants and curved Bernstein-Gelfand-Gelfand sequences
Abstract
We give a simple construction of the Bernstein-Gelfand-Gelfand sequences of natural differential operators on a manifold equipped with a parabolic geometry. This method permits us to define the additional structure of a bilinear differential cup product on this sequence, satisfying a Leibniz rule up to curvature terms. It is not associative, but is part of an A-infinity algebra of multilinear differential operators, which we also obtain explicitly. We illustrate the construction in the case of conformal differential geometry, where the cup product provides a wide-reaching generalization of helicity raising and lowering for conformally invariant field equations.
Cite
@article{arxiv.math/0001158,
title = {Differential invariants and curved Bernstein-Gelfand-Gelfand sequences},
author = {David M. J. Calderbank and Tammo Diemer},
journal= {arXiv preprint arXiv:math/0001158},
year = {2007}
}
Comments
AMS-LaTeX 31 pages; improved proof of A-infinity stuff; references added; corrected deformation theory discussion