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

Martintxo Saralegi-Aranguren (1) , Robert Wolak (2)

1 LML - Laboratoire de Mathématiques de Lens
2 Instytut Matematyki

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).

Domains: Mathematics [math]; Differential Geometry [math.DG]; Mathematics [math]; Algebraic Topology [math.AT]

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