Volume 12, issue 3 (2012)

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Brunnian braids on surfaces

Valery G Bardakov, Roman Mikhailov, Vladimir V Vershinin and Jie Wu

Algebraic & Geometric Topology 12 (2012) 1607–1648
Abstract

We determine a set of generators for the Brunnian braids on a general surface $M$ for $M\ne {S}^{2}$ or $ℝ{P}^{2}$. For the case $M={S}^{2}$ or $ℝ{P}^{2}$, a set of generators for the Brunnian braids on $M$ is given by our generating set together with the homotopy groups of a $2$–sphere.

Keywords
braid group, Brunnian braid, homotopy group, symmetric commutator subgroup
Mathematical Subject Classification 2010
Primary: 57M07, 57M99
Secondary: 20F36, 55Q40