Brunnian braids on surfaces

We determine a set of generators for the Brunnian braids on a general surface $M$ for $M \neq S^{2}$ 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.

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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

Volume 12, issue 3 (2012)

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

Abstract