Revistes Catalanes amb Accés Obert (RACO)

Pure braid subgroups of braided Thompson's groups

T. Brady, Josep Burillo, S. Cleary, M. Stein
DOI: 74464


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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