The Sigma invariants for the Golden Mean Thompson group

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.

19 pages. v2: Major revision after referee's comments, corrected inacurracies/inconsistencies throughout the text, improved proof of the main theorem, restated results on Sigma invariants and characters for clarity, expanded on related work. Final version, to appear in the New York Journal of Mathematics