Poincaré duality of the basic intersection cohomology of a Killing foliation

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

1 LML - Laboratoire de Mathématiques de Lens
2 Institute of Mathematics Jagiellonian University

We prove that the basic intersection cohomology $IH^*_{\overline{p}}(M / \mathcal{F})$, where $\mathcal{F}$ is the singular foliation determined by an isometric action of a Lie group $G$ on the compact manifold $M$, verifies the Poincaré Duality Property.

Keywords: Singular Foliation; Intersection Cohomology; Lie Group Actions

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

Martintxo Saralegi-Aranguren, Robert Wolak. Poincaré duality of the basic intersection cohomology of a Killing foliation. Monatshefte für Mathematik, 2016, 180, pp.145-166. ⟨10.1007/s00605-016-0882-4⟩. ⟨hal-00936000⟩