Boundary actions of outer automorphism groups of Thompson-like groups

Chris Bruce; Xin Li; Takuya Takeishi

Paper

Boundary actions of outer automorphism groups of Thompson-like groups

Abstract

For every Cuntz--Krieger groupoid, we show that there is a topologically free boundary action of the outer automorphism group of its topological full group on the Hilbert cube. In particular, these outer automorphism groups, including the outer automorphism groups of all Higman--Thompson groups, are C*-simple.