On the topological invariance of the basic cohomology (Q1318028)

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 \({\mathcal F}\).