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

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

2004-01-28

arxiv.org/abs/math/0401407v4

Ann. Polon. Math. 89(2006), 203-246

Mathematics

Differential Geometry

Scientific paper

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 Poincar\'e Duality. This duality includes two well-known situations: -- Poincar\'e Duality for basic cohomology (the action $\Phi$ is almost free). -- Poincar\'e Duality for intersection cohomology (the group $G$ is compact and connected).

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