Mathematics – Differential Geometry
Scientific paper
2000-01-27
J.Reine Angew.Math. 537 (2001) 67-103
Mathematics
Differential Geometry
AMS-LaTeX 31 pages; improved proof of A-infinity stuff; references added; corrected deformation theory discussion
Scientific paper
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.
Calderbank David M. J.
Diemer Tammo
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