Open Access
2008 Pure braid subgroups of braided Thompson's groups
Tom Brady, José Burillo, Sean Cleary, Melanie Stein
Publ. Mat. 52(1): 57-89 (2008).


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.


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Tom Brady. José Burillo. Sean Cleary. Melanie Stein. "Pure braid subgroups of braided Thompson's groups." Publ. Mat. 52 (1) 57 - 89, 2008.


Published: 2008
First available in Project Euclid: 17 December 2007

zbMATH: 1185.20043
MathSciNet: MR2384840

Primary: 20F65
Secondary: 20E22 , 20F05 , 20F36

Keywords: braid groups , braided tree diagrams , pure braids , Thompson’s groups

Rights: Copyright © 2008 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.52 • No. 1 • 2008
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