An exotic group with the Haagerup property

TL;DR

This paper proves that a specially constructed infinite discrete group, derived from a Euclidean Tits building of type A2, possesses the Haagerup property, which has implications for its geometric and analytical properties.

Contribution

It introduces a new example of an infinite discrete group with the Haagerup property, constructed via surgery on a Euclidean Tits building of type A2.

Findings

The group has the Haagerup property.

The construction uses surgery on Euclidean Tits buildings.

This provides new examples of groups with the Haagerup property.

Abstract

We prove the Haagerup property for an infinite discrete group constructed using surgery on a Euclidean Tits building of type $\tilde A_2$.