# 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).
Type de document :
Article dans une revue
Annales Polonici Mathematici, 2006, 89, pp.203-246
Domaine :

https://hal-univ-artois.archives-ouvertes.fr/hal-00869651
Contributeur : Martintxo Saralegi-Aranguren <>
Soumis le : jeudi 3 octobre 2013 - 18:18:46
Dernière modification le : mercredi 27 juillet 2016 - 14:48:48

### 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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