Metric Properties of the Braided Thompson’s Groups
نویسنده
چکیده
Braided Thompson’s groups are finitely presented groups introduced by Brin and Dehornoy which contain the ordinary braid groups Bn, the finitary braid group B∞ and Thompson’s group F as subgroups. We describe some of the metric properties of braided Thompson’s groups and give upper and lower bounds for word length in terms of the number of strands and the number of crossings in the diagrams used to represent elements.
منابع مشابه
The algebra of strand splitting. I. A braided version of Thompson’s group V
We construct a braided version BV of Thompson’s group V that surjects onto V . The group V is the third of three well known groups F , T and V created by Thompson in the 1960s that have been heavily studied since. See [6] and Section 4 of [5] for an introduction to Thompson’s groups. The group V is a subgroup of the homeomorphism group of the Cantor set C. It is generated by involutions [2, Sec...
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We describe pure braided versions of Thompson’s group F . These groups, BF and B̂F , are subgroups of the braided versions of Thompson’s group V , introduced by Brin and Dehornoy. Unlike V , elements of F are order-preserving self-maps of the interval and we use pure braids together with elements of F thus preserving order. We define these groups and give normal forms for elements and describe i...
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