Some H1F-groups with unbounded torsion and a conjecture of Kropholler and Mislin

TL;DR

This paper investigates a conjecture about groups acting on finite-dimensional complexes, extending its validity to a broad class of groups with unbounded torsion, beyond previously known cases.

Contribution

It demonstrates that the Kropholler-Mislin conjecture holds for a large subclass of groups with unbounded torsion, expanding the scope of known results.

Findings

The conjecture is verified for a broad class of groups with unbounded torsion.

The paper introduces a large class U of groups containing known examples.

It extends the validity of the conjecture beyond groups with bounded torsion.

Abstract

Kropholler and Mislin conjectured that groups acting admissibly on a finite-dimensional G-CW-complex with finite stabilisers admit a finite-dimensional model for E_FG, the classifying space for proper actions. This conjecture is known to hold for groups with bounded torsion. In this note we consider a large class of groups U containing the above and many known examples with unbounded torsion. We show that the conjecture holds for a large subclass of U.