Finitness of the basic intersection cohomology of a Killing foliation

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

1 LML - Laboratoire de Mathématiques de Lens
2 Instytut Matematyki

We prove that the basic intersection cohomology $ {I\! \! H}^{^{*}}_{_{\overline{p}}}{\left( M/\mathcal{F} \right)}, $ where $\mathcal{F}$ is the singular foliation determined by an isometric action of a Lie group $G$ on the compact manifold $M$, is finite dimensional.

Keywords: Intersection cohomology; Lie groups actions

Domains: Differential Geometry [math.DG]

Martintxo Saralegi-Aranguren, Robert Wolak. Finitness of the basic intersection cohomology of a Killing foliation. Mathematische Zeitschrift, 2012, 272, pp.443-457. ⟨10.1007/s00209-011-0942-3⟩. ⟨hal-00443657⟩