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 ≠ ℝP2, 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.
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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Vol. 286, pp. 22–39.
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Bardakov, V.G., Vershinin, V.V. & Wu, J. On Cohen braids. Proc. Steklov Inst. Math. 286, 16–32 (2014). https://doi.org/10.1134/S0081543814060029
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DOI: https://doi.org/10.1134/S0081543814060029