IUMJ

Title: Metric properties of braided Thompson's groups

Authors: Jose Burillo and Sean Cleary

Issue: Volume 58 (2009), Issue 2, 605-616

Abstract:

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.