New examples of finitely presented groups with strong fixed point properties

TL;DR

This paper presents a simple example of a finitely presented group that cannot act freely without fixed points on finite-dimensional CAT(0) spaces, highlighting limitations of group actions in geometric group theory.

Contribution

Provides an accessible example of a finitely presented group with strong fixed point properties, expanding understanding of group actions on CAT(0) spaces.

Findings

The group cannot act without fixed points on finite-dimensional CAT(0) spaces.

Simplifies the construction of such groups compared to previous methods.

Highlights limitations of group actions in geometric contexts.

Abstract

The aim of this note is to give an easy example of a finitely presented group that cannot act without a fix point on a CAT(0) space of finite dimension. Such an example has been recently constructed by Arjantseva et al., using other techniques