The Sigma invariants for the Golden Mean Thompson group

TL;DR

This paper calculates the BNSR-invariants for the irrational slope Thompson's group $F_{\tau}$ using a method by Bieri, Geoghegan, and Kochloukova, addressing a problem posed by Strebel.

Contribution

It establishes conditions under which the Sigma invariants of $F_{\tau}$ match those of a finite index subgroup, advancing understanding of these invariants.

Findings

Calculated BNSR-invariants for $F_{\tau}$

Established conditions for invariants to coincide with subgroup invariants

Addressed a problem posed by Strebel

Abstract

We use a method of Bieri, Geoghegan and Kochloukova to calculate the BNSR-invariants for the irrational slope Thompson's group $F_{\tau}$. To do so we establish conditions under which the Sigma invariants coincide with those of a subgroup of finite index, addressing a problem posed by Strebel.