Year: 2019
Type: preprint
Abstract: The higher-dimensional Thompson groups $nV$, for $n \geq 2$, were introduced by Brin in 2005. We provide new presentations for each of these infinite simple groups. The first is an infinite presentation, analogous to the Coxeter presentation for the finite symmetric group, with generating set equal to the set of transpositions in $nV$ and reflecting the self-similar structure of $n$-dimensional Cantor space. We then exploit this infinite presentation to produce further finite presentations that are considerably smaller than those previously known.
Source: arXiv (Cornell University)
Author: Quick, Martyn
Institution: University of St Andrews
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2910075879