On the topological invariance of the basic cohomology
type: Item
instance of: scholarly article
title: On the topological invariance of the basic cohomology
zbMATH Open document ID: 0793.57016
DOI: 10.1007/BF01444906
published in: Mathematische Annalen
publication date: 1994-08-25T00:00:00Z
full work available at URL: https://eudml.org/doc/165061
review text: The algebra of basic differential forms of a foliated manifold \((M,{\mathcal F})\) is a differential complex whose homology \(H^* (M/{\mathcal F})\) is called the basic cohomology of \({\mathcal F}\). In this paper we show that the algebra \(H^* (M/{\mathcal F})\) is a topological invariant for complete Riemannian foliations. The main tools used to prove this assertion are: (i) Haefliger's description of a tubular neighbourhood of a leaf closure in the case \(M\) is a solvmanifold and (ii) a spectral sequence which computes \(H^* (M/{\mathcal F})\) from the basic cohomology of the foliation restricted to a certain type of neighbourhoods of the leaf closures of \({\mathcal F}\).
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 55T99
zbMATH DE Number: 537228
zbMATH Keywords: algebra of basic differential forms of a foliated manifold
zbMATH Keywords: basic cohomology
zbMATH Keywords: topological invariant
zbMATH Keywords: complete Riemannian foliations
zbMATH Keywords: leaf closure
zbMATH Keywords: spectral sequence
author: A. El Kacimi Alaoui
author: Marcel Nicolau
MaRDI profile type: Publication
cites work: Q3961493
cites work: Q5658847
cites work: Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
cites work: De Rham-Hodge theory for Riemannian foliations
cites work: Q3977313
cites work: The Existence of Complete Riemannian Metrics
cites work: Foliated manifolds with bundle-like metrics
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description: scientific article; zbMATH DE number 537228