Brunnian braids on surfaces

Bardakov, Valery G¹ ; Mikhailov, Roman² ; Vershinin, Vladimir V³ ; Wu, Jie⁴

¹Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
²Steklov Mathematical Institute, Gubkina 8, Moscow, 119991, Russia
³Département des Sciences Mathématiques, Université Montpellier II, Place Eugène Bataillon, 3, 34095 Montpellier cedex 5, France, (and Sobolev Institute of Mathematics)
⁴Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117542, Singapore

Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1607-1648

Résumé

We determine a set of generators for the Brunnian braids on a general surface M for M≠S2 or ℝ P2. For the case M = S2 or ℝ P2, 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.

Détail

DOI : 10.2140/agt.2012.12.1607

Classification : 57M07, 57M99, 20F36, 55Q40
Keywords: braid group, Brunnian braid, homotopy group, symmetric commutator subgroup

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