Higher dimensional Thompson groups have Serre's property FA

TL;DR

This paper proves that all higher dimensional Thompson groups nV possess Serre's property FA, extending previous results known for the classical Thompson group V, and thus contributes to understanding their fixed point properties.

Contribution

The paper establishes that all higher dimensional Thompson groups nV have Serre's property FA, generalizing prior results from the classical case of V.

Findings

nV groups have Serre's property FA for all n

Generalizes Farley's result for V to higher dimensions

Enhances understanding of fixed point properties in these groups

Abstract

The Thompson group V is a subgroup of the homeomorphism group of the Cantor set. Brin defined higher dimensional Thompson groups nV as generalizations of V. We prove that nV has Serre's property FA, for every n. This is a generalization of the corresponding result of Farley, who studied V.