Presentations for the higher dimensional Thompson's groups nV

Details Presentations for the higher dimensional Thompson's groups nV Presentations for the higher dimensional Thompson's groups nV

2011-05-18

arxiv.org/abs/1105.3714v1

Mathematics

Group Theory

18 pages, 2 figures

Scientific paper

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]).

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