Pure braid subgroups of braided Thompson's groups

Abstract

We describe 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, 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.

26 pages, 6 figures, with updated bibliography

References in corpus (3)

• The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V
• The Algebra of Strand Splitting. II. A Presentation for the Braid Group on One Strand
• The group of parenthesized braids