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A singular Poincare lemma

Eva Miranda·Vu Ngoc San
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Abstract

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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Eva Miranda, Vu Ngoc San. 2004-05-23. A singular Poincare lemma. https://arxiv.org/abs/math/0405430

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