Presentations for the higher-dimensional Thompson groups nV

Johanna Hennig and Francesco Matucci

Vol. 257 (2012), No. 1, 53–74

DOI: 10.2140/pjm.2012.257.53

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 = 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).

Keywords

Thompson groups, groups of piecewise-linear homeomorphisms, finiteness properties, finite presentations

Mathematical Subject Classification 2010

Primary: 20F05, 20F65

Milestones

Received: 18 May 2011

Revised: 13 February 2012

Accepted: 21 February 2012

Published: 19 June 2012