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Cohomology of Lie foliations. (English) Zbl 0646.57016
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