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

Bieri, Geoghegan and Kochloukova computed the BNSR-invariants ${\mathrm{\Sigma }}^m(F)$ 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.