A Singular Poincaré Lemma


We prove a Poincaré lemma for a set of r smooth functions on a 2n-dimensional smooth manifold satisfying a commutation relation determined by r singular vector fields associated to a Cartan subalgebra of sp(2r, R). This result has a natural interpretation in terms of the cohomology associated to the infinitesimal deformation of a completely integrable… (More)