A SHORT ACCOUNT OF WHY THOMPSON'S GROUP F IS OF TYPE F_∞

In 1984 Brown and Geoghegan proved that Thompson's group F is of type F_∞, making it the first example of an infinite dimensional torsion-free group of type F_∞. Over the decades a different, shorter proof has emerged, which is more streamlined and generalizable to other groups. It is difficult, however, to isolate this proof in the literature just for F itself, with no complicated generalizations considered and no additional properties proved. The goal of this expository note then is to present the “modern” proof that F is of type F∞, and nothing else.