The Basilica Thompson group is not finitely presented

TL;DR

This paper proves that the Basilica Thompson group is not finitely presented and not of type FP_2, using techniques involving CAT(0) cube complexes to analyze its subcomplexes.

Contribution

It introduces new methods for proving non-simple connectedness of subcomplexes in CAT(0) cube complexes, demonstrating the non-finite presentability of the Basilica Thompson group.

Findings

Basilica Thompson group is not finitely presented

The group is not of type FP_2

Develops techniques for analyzing subcomplexes in CAT(0) cube complexes

Abstract

We show that the Basilica Thompson group introduced by Belk and Forrest is not finitely presented, and in fact is not of type FP_2. The proof involves developing techniques for proving non-simple connectedness of certain subcomplexes of CAT(0) cube complexes.