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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 MS2 or P2. For the case M = S2 or 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.

Keywords
braid group, Brunnian braid, homotopy group, symmetric commutator subgroup
Mathematical Subject Classification 2010
Primary: 57M07, 57M99
Secondary: 20F36, 55Q40
References
Publication
Received: 18 December 2011
Revised: 6 May 2012
Accepted: 11 May 2012
Published: 25 July 2012
Authors
Valery G Bardakov
Sobolev Institute of Mathematics
Novosibirsk
630090
Russia
Roman Mikhailov
Steklov Mathematical Institute
Gubkina 8
Moscow
119991
Russia
Vladimir V Vershinin
Département des Sciences Mathématiques
Université Montpellier II
Place Eugène Bataillon, 3
34095 Montpellier cedex 5
France
(and Sobolev Institute of Mathematics)
Jie Wu
Department of Mathematics
National University of Singapore
2 Science Drive 2
Singapore 117542
Singapore
http://www.math.nus.edu.sg/~matwujie