Amenability of Thompson's group F

Determine whether Thompson's group F is amenable.

Background

The paper introduces Thompson's groups F, T, and V and notes that these groups exhibit several surprising properties. As part of this context, the author highlights a longstanding unresolved problem concerning Thompson's group F: whether it is amenable. Amenability, a central concept in geometric group theory, asks for the existence of an invariant mean on the group.

Although the main focus of the paper is the divergence function of higher-dimensional Thompson groups nV, the amenability of F is mentioned to illustrate the broader landscape of challenging questions surrounding Thompson-type groups.