Pure braid subgroups of braided Thompson's groups

Details Pure braid subgroups of braided Thompson's groups Pure braid subgroups of braided Thompson's groups

2006-03-22

arxiv.org/abs/math/0603548v2

Mathematics

Group Theory

26 pages, 6 figures, with updated bibliography

Scientific paper

We describe pure braided versions of Thompson's group F. These groups, $BF$ and $\hat{BF}$, are subgroups of the braided versions of Thompson's group V, introduced by Brin and Dehornoy. Unlike V, elements of F are order-preserving self-maps of the interval and we use pure braids together with elements of F thus preserving order. We define these groups and give normal forms for elements and describe infinite and finite presentations of these groups.

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