Non-inner amenability of the Thompson groups T and V
  In this paper we prove that the Thompson groups $T$ and $V$ are not inner amenable. In particular, their group von Neumann algebras do not have property $\Gamma$. Moreover, we prove that if the reduced group $C^\ast$-algebra of $T$ is simple, then the Thompson group $F$ is non-amenable. Furthermore, we give a few new equivalent characterizations of amenability of $F$. 
Uffe Haagerup and Kristian Knudsen Olesen
math.OA math.GR