A Poincaré lemma in geometric quantisation (Q2438159)

The aim of this paper is to prove that, notwithstanding the fact that local closed forms are not necessarily locally exact for foliated cohomology of singular foliations, one can still prove a Poincaré lemma for the twisted (or Kostant) complex when the foliation is given by an integrable system with nondegenerate singularities. In particular, this allow to compute the geometric quantisation by calculating the cohomology of the Kostant complex from the geometrical properties of this type of singularities.