Simple groups with strong fixed-point properties

TL;DR

This paper introduces finitely generated torsion-free groups that exhibit strong fixed-point properties, ensuring any finite-dimensional CW-complex action with finite Betti numbers has a fixed point.

Contribution

It presents new examples of groups with universal fixed-point properties for actions on finite-dimensional CW-complexes.

Findings

Existence of finitely generated torsion-free groups with fixed-point properties

Any action on finite-dimensional CW-complexes with finite Betti numbers has a fixed point

Advances understanding of fixed-point phenomena in geometric group theory

Abstract

We exhibit finitely generated torsion-free groups for which any action on any finite-dimensional CW-complex with finite Betti numbers has a global fixed point.