Abstract
For a general connected surface M and an arbitrary braid α from the surface braid group Bn−1(M), we study the system of equations d1β = … = dnβ = α, where the operation di is the removal of the ith strand. We prove that for M ≠ S2 and M ≠ ℝP2, this system of equations has a solution β ∈ Bn(M) if and only if d1α = … = dn−1α. We call the set of braids satisfying the last system of equations Cohen braids. We study Cohen braids and prove that they form a subgroup. We also construct a set of generators for the group of Cohen braids. In the cases of the sphere and the projective plane we give some examples for a small number of strands.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the Steklov Institute of Mathematics
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.
