Examples of finitely presented groups with strong fixed point properties and property (T)

TL;DR

This paper constructs a finitely presented group with property (T) that cannot act on reasonable spaces, using a generalized Hall embedding theorem with weakened simplicity requirements.

Contribution

It introduces a new method to build finitely presented groups with property (T) that lack certain action capabilities, expanding understanding of fixed point properties.

Findings

Constructed a finitely presented group with property (T) that cannot act on reasonable spaces.

Generalized Hall embedding theorem used to achieve the construction.

Demonstrated the possibility of groups with strong fixed point properties but limited actions.

Abstract

We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the simplicity requirement.