Thompson's group F is not strongly amenable

TL;DR

This paper demonstrates that Thompson's group F admits a topological action on a compact metric space that is proximal and fixed-point free, revealing new dynamical properties of the group.

Contribution

It introduces a novel topological action of Thompson's group F that is proximal and has no fixed points, advancing understanding of its dynamical behavior.

Findings

Thompson's group F admits a proximal, fixed-point free action on a compact metric space.

The action reveals new dynamical properties of F.

This challenges previous assumptions about fixed points in such actions.

Abstract

We show that Thompson's group $F$ has a topological action on a compact metric space that is proximal and has no fixed points.