Metric properties of the braided Thompson's groups

Details Metric properties of the braided Thompson's groups Metric properties of the braided Thompson's groups

2007-10-29

arxiv.org/abs/0710.5518v1

Mathematics

Group Theory

10 pages, 5 figures

Scientific paper

Braided Thompson's groups are finitely presented groups introduced by Brin and Dehornoy which contain the ordinary braid groups $B_n$, the finitary braid group $B_{\infty}$ 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.

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