Cohomology of Lie foliations. (English) Zbl 0646.57016

Masa, X.

Differential geometry, Proc. 5th Int. Colloq., Santiago de Compostela/Spain 1984, Res. Notes Math. 131, 211-214 (1985).

[For the entire collection see Zbl 0637.00004.]
The de Rham complex on a manifold M with a foliation \({\mathcal F}\) becomes a filtered complex when one says that a k-form \(\omega\) on M has filtration \(\geq a\) if \(\omega (v_ 1,...,v_ k)=0\) whenever \(k-a+1\) vectors among \(v_ i's\) are tangent to \({\mathcal F}\). The author computes the spectral sequence of this filtered complex for Lie foliations and obtains some consequences.

Reviewer: P.Walczak

MSC:

57R30	Foliations in differential topology; geometric theory
58A12	de Rham theory in global analysis
55T99	Spectral sequences in algebraic topology

Keywords:

de Rham complex on a manifold M with a foliation; spectral sequence; Lie foliations