Metric properties of braided Thompson's groups Jose BurilloSean Cleary 20F6520F36Thompson's groupsbraid groups 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. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3468 10.1512/iumj.2009.58.3468 en Indiana Univ. Math. J. 58 (2009) 605 - 616 state-of-the-art mathematics http://iumj.org/access/