Vol. 257, No. 1, 2012

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Presentations for the higher-dimensional Thompson groups nV

Johanna Hennig and Francesco Matucci

Vol. 257 (2012), No. 1, 53–74

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).

Thompson groups, groups of piecewise-linear homeomorphisms, finiteness properties, finite presentations
Mathematical Subject Classification 2010
Primary: 20F05, 20F65
Received: 18 May 2011
Revised: 13 February 2012
Accepted: 21 February 2012
Published: 19 June 2012
Johanna Hennig
Department of Mathematics
University of California, San Diego
9500 Gilman Drive
La Jolla, CA 92093
United States
Francesco Matucci
Department of Mathematics
University of Virginia
325 Kerchof Hall
Charlottesville, VA 22904
United States