On Cohen braids

Valery Bardakov; Vladimir Vershinin; Jie Wu

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arXiv · 1312.2924

On Cohen braids

Valery Bardakov·Vladimir Vershinin·Jie Wu

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Abstract

For a general surface $M$ and an arbitrary braid $α$ from the surface braid group $B_{n-1}(M)$ we study the system of equations $d_1β=\cdots=d_{n}β=α, $ where operation $d_i$ is deleting of $i$-th strand. We obtain that if $M\not=S^2$ or $\mathbb RP^2$ this system of equations has a solution $β\in B_{n}(M)$ if and only if $d_1α=\ldots=d_nα. $ The set of braids satisfying the last system of equations we call Cohen braids. We also construct a set of generators for the groups of Cohen braids. In the cases of the sphere and the projective plane we give some examples for the small number of strands.

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Valery Bardakov, Vladimir Vershinin, Jie Wu. 2013-12-10. On Cohen braids. https://arxiv.org/abs/1312.2924

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