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

Martintxo Saralegi-Aranguren, Robert Wolak
2006 Annales Polonici Mathematici  
We study the cohomology properties of the singular foliation F determined by an action Φ : G×M → 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 IH * p (M/F ) is finite-dimensional and satisfies the Poincaré duality. This duality includes two well known situations: • Poincaré duality for basic cohomology (the action Φ is almost free). • Poincaré duality for intersection cohomology (the
more » ... G is compact and connected). 2000 Mathematics Subject Classification: 53C12, 57R30, 55N33, 58A35, 22Fxx.
doi:10.4064/ap89-3-1 fatcat:a6nsgq7sdfbb5ldfwzai3h556i