Presentations for the higher-dimensional Thompson groups<i>nV</i>

Abstract

M. G. Brin has introduced the higher-dimensional Thompson groups nV that are generalizations to the Thompson group V of self-homeomorphisms of the Cantor set and found a finite set of generators and relations in the case n=D 2. We show how to generalize his construction to obtain a finite presentation for every positive integer n. As a corollary, we obtain another proof that the groups nV are simple (first proved by Brin). © 2012 by Pacific Journal of Mathematics.