|
|||||
|
|
On Cohen braids |
|
| Authors: | V. G. Bardakov V. V. Vershinin J. Wu |
| Affiliation: | 1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia 2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia 3. Laboratory of Quantum Topology, Chelyabinsk State University, ul. Brat’ev Kashirinykh 129, Chelyabinsk, 454001, Russia 4. Département des Sciences Mathématiques, Université Montpellier 2, Place Eugène Bataillon, 34095, Montpellier cedex 5, France 5. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore, 119076, Singapore |
| Abstract: | For a general connected surface M and an arbitrary braid α from the surface braid group B n?1(M), we study the system of equations d 1 β = … = d n β = α, where the operation d i is the removal of the ith strand. We prove that for M ≠ S 2 and M ≠ ?P2, this system of equations has a solution β ∈ B n (M) if and only if d 1 α = … = d n?1 α. 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. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |