Fast growth in the Følner function for Thompson’s group $F$

Abstract

The purpose of this note is to prove a lower bound on the growth of Følner functions for Richard Thompson’s group $F$. Specifically I will prove that, for any finite generating set $\Gamma \subseteq F$, there is a constant $C$ such that Føl${}_{F,\Gamma }(C^n)\ge$ exp${}_n(0)$.