Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.