A singular Poincaré lemma

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 a...

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Bibliographic Details
Authors: Miranda Galcerán, Eva, Vu Ngoc, S.
Format: article
Status:Published version
Publication Date:2005
Country:España
Institution:Universidad de Barcelona
Repository:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/9175
Online Access:https://hdl.handle.net/2445/9175
Access Level:Open access
Keyword:Formes diferencials
Geometria algebraica
Poincaré lemma
Differential forms
Description
Summary: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.