Finitness of the basic intersection cohomology of a Killing foliation

TL;DR

This paper proves that the basic intersection cohomology associated with a Killing foliation induced by an isometric Lie group action on a compact manifold is finite dimensional, advancing understanding of the topological invariants of singular foliations.

Contribution

It establishes the finite dimensionality of basic intersection cohomology for Killing foliations generated by isometric Lie group actions on compact manifolds.

Findings

Basic intersection cohomology is finite dimensional.

The result applies to singular foliations from isometric group actions.

Provides new insights into the topology of Killing foliations.

Abstract

We prove that the basic intersection cohomology $ {I H}^{^{*}}_{_{\bar{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 $M$, is finite dimensional.