# The BIC of a singular foliation defined by an abelian group of isometries

Abstract : We study the cohomology properties of the singular foliation $\F$ determined by an action $\Phi \colon G \times M\to M$ where the abelian Lie group $G$ preserves a riemannian metric on the compact manifold $M$. More precisely, we prove that the basic intersection cohomology $\lau{\IH}{*}{\per{p}}{\mf}$ is finite dimensional and verifies the Poincaré Duality. This duality includes two well-known situations: -- Poincaré Duality for basic cohomology (the action $\Phi$ is almost free). -- Poincaré Duality for intersection cohomology (the group $G$ is compact and connected).
Document type :
Journal articles
Domain :

https://hal-univ-artois.archives-ouvertes.fr/hal-00869651
Contributor : Martintxo Saralegi-Aranguren <>
Submitted on : Thursday, October 3, 2013 - 6:18:46 PM
Last modification on : Friday, September 4, 2020 - 2:46:03 PM

### Citation

M. Saralegi-Aranguren, R. Wolak. The BIC of a singular foliation defined by an abelian group of isometries. Annales Polonici Mathematici, 2006, 89, pp.203-246. ⟨hal-00869651⟩

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