Publicacions Matemàtiques

Pure braid subgroups of braided Thompson's groups

Tom Brady, José Burillo, Sean Cleary, and Melanie Stein

Full-text: Open access


We describe some properties of braided generalizations of Thompson's groups, introduced by Brin and Dehornoy. We give slightly different characterizations of the braided Thompson's groups $BV$ and $\widehat{BV}$ which lead to natural presentations which emphasize one of their subgroup-containment properties. We consider pure braided versions of Thompson's group $F$. These groups, $BF$ and $\widehat{BF}$, are subgroups of the braided versions of Thompson's group $V$. Unlike $V$, elements of $F$ are order-preserving self-maps of the interval and we use pure braids together with elements of $F$ thus again preserving order. We define these pure braided groups, give normal forms for elements, and construct infinite and finite presentations of these groups.

Article information

Publ. Mat., Volume 52, Number 1 (2008), 57-89.

First available in Project Euclid: 17 December 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 20F36: Braid groups; Artin groups 20F05: Generators, relations, and presentations 20E22: Extensions, wreath products, and other compositions [See also 20J05]

Thompson’s groups braid groups pure braids braided tree diagrams


Brady, Tom; Burillo, José; Cleary, Sean; Stein, Melanie. Pure braid subgroups of braided Thompson's groups. Publ. Mat. 52 (2008), no. 1, 57--89.

Export citation