# Higher-Dimensional Higman-Thompson Group

Specialeforsvar ved Sebastian Holmegaard Schwarze

Titel: Higher-Dimensional Higman-Thompson Group

Abstract: The aim of this thesis is to investigate the homology of the higher-dimensional Higman-Thompson groups - a family of groups covering the higher-dimensional Thompson groups defined by M. G. Brin and the Higman-Thompson defined by Higman, both as generalizations of Thompson's group $V$. The general idea is to try to apply some of the methods used in a paper by M. Szyik and N. Wahl, in which the homology of one-dimensional Higman-Thompson groups is computed, to the more general higher-dimensional Higman-Thompson groups. This has involved firstly describing the higher-dimensional Higman-Thompson groups in the framework of operads, similar to what is done by W. Thumann and then constructing a generalization of a functor used by M. Szyik and N. Wahl to compute the stable homology of the one-dimensional Higman-Thompson groups.

Vejleder:  Nathalie Wahl
Censor:    Iver Mølgaard Ottosen, AAU