On a Poincare lemma for foliations

Abstract

In this paper we revisit a Poincare lemma for foliated forms, with respect to a regular foliation, and compute the foliated cohomology for local models of integrable systems with singularities of nondegenerate type. A key point in this computation is the use of some analytical tools for integrable systems with nondegenerate singularities, including a Poincare lemma for the deformation complex associated to this singular foliation.

23 pages, an error in proposition 5.1 in the former version was detected and the paper has been rewritten accordingly

References in corpus (1)

• Symplectic Techniques for Semiclassical Completely Integrable Systems

Cited by in corpus (3)

• Non-commutative integrable systems on $b$-symplectic manifolds
• A Poincare lemma in Geometric Quantisation
• Darboux normal form theorem as an example of Liouville integrability theorem