The $\Sigma$-invariants of Thompson's group $F$ via Morse theory

Abstract

Bieri, Geoghegan and Kochloukova computed the BNSR-invariants ${\Sigma }^m(F)$ of Thompson's group $F$ for all $m$. We recompute these using entirely geometric techniques, making use of the Stein--Farley CAT(0) cube complex on which $F$ acts.

17 pages, 2 figures. v2: updated to add an acknowledgment (and some very minor edits)