A singular Poincare lemma

Details A singular Poincare lemma A singular Poincare lemma

2004-05-23

arxiv.org/abs/math/0405430v1

Mathematics

Symplectic Geometry

18 pages

Scientific paper

We prove a Poincare 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 $\frak{sp}(2r,\mathbb R)$.
This result has a natural interpretation in terms of the cohomology associated
to the infinitesimal deformation of a completely integrable system.

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