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Metric properties of
higher-dimensional Thompson’s groups
José Burillo and Sean Cleary |
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Vol. 248 (2010), No. 1, 49–62
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Abstract |
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Higher-dimensional Thompson’s groups nV are finitely presented groups that generalize dyadic self-maps of the unit interval to dyadic self-maps of n-dimensional unit cubes. We describe some of the metric properties of these groups. We describe their elements based upon tree-pair diagrams and give upper and lower bounds for word length in terms of the size of the diagrams. Though these bounds are somewhat separated, we show that there are elements realizing the lower bounds and that the fraction of elements that are close to the upper bound converges to 1, showing that the bounds are optimal and that the upper bound is generically achieved. |
Keywords
Thompson’s groups
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Mathematical Subject Classification 2000
Primary: 20F65
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Milestones
Received: 21 October 2008
Revised: 6 October 2009
Accepted: 14 October 2009
Published: 1 October 2010
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Authors |
| José Burillo | |
| Departament de Matemàtica Aplicada
IV Universitat Politècnica de Catalunya Escola Politècnica, Superior de Castelldefels Avda. Del Canal Olímpic 15 08860 Castelldefels Spain |
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| http://www-ma4.upc.edu/~burillo/ | |
| Sean Cleary | |
| Department of Mathematics The City College of New York Convent Ave at 138th St. New York, NY 10031 United States |
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| http://www.sci.ccny.cuny.edu/~cleary | |
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