Revistes Catalanes amb Accés Obert (RACO)

Pure braid subgroups of braided Thompson's groups

T. Brady, Josep Burillo, S. Cleary, M. Stein


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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