Automorphism tower of groups of homeomorphism of Cantor space

Abstract:

The class of full and sufficiently transitive (i.e. flexible) groups of homeomorphisms of Cantor space contains many groups of interest including  generalisations of the Higman-Thompson groups G_{n,r}, and the Rational group R_2 of Grigorchuk, Nekrashevych, and Suchanskiı̆. We will introduce this class of groups and go on to describe recent results on the automorphism tower of such groups. For the groups Gn,r our result can be seen as extending results of Brin and Guzmán for Thompson’s group T and generalisations of Thompson’s group F.