Presentations for the Higher Dimensional Thompson's groups nV

Pacific Journal of Mathematics, 257(1) (2012), 53--74
http://dx.doi.org/10.2140/pjm.2012.257.53 (preprint - http://arxiv.org/abs/1105.3714)

In his papers [2], [3] Brin introduced the higher dimensional Thompson groups nV which are generalizations to the Thompson's group V of self-homeomorphisms of the Cantor set and found a finite set of generators and relations in the case n = 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 in [4]).