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Proceedings of the London Mathematical Society Advance Access originally published online on March 17, 2009
Proceedings of the London Mathematical Society 2009 99(3):521-556; doi:10.1112/plms/pdp005
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© 2009 London Mathematical Society

Artin braid groups and homotopy groups

Jingyan Li

Institute of Mathematics and Physics
Shijiazhuang Railway Institute
Shijiazhuang 050043
China
yanjinglee@163.com

Jie Wu

Department of Mathematics
National University of Singapore
2 Science Drive 2
Singapore 117542
Singapore
www.math.nus.edu.sg/~matwujie

Received 9 May 2008. Revision received 23 December 2008.

We study the Brunnian subgroups and the boundary Brunnian subgroups of the Artin braid groups. The general higher homotopy groups of the sphere are given by mirror symmetric elements in the quotient groups of the Artin braid groups modulo the boundary Brunnian braids, as well as given as summands of the centres of the quotient groups of Artin pure braid groups modulo boundary Brunnian braids. The results give new connections between the braid groups and the general higher homotopy groups of spheres.

The first author was partially supported by the Academic Research Fund from Shijiazhuang Railway Institute. The second author was partially supported by the Academic Research Fund of the National University of Singapore (R-146-000-101-112).

2000 Mathematics Subject Classification 20F36, 55Q40, 55U10 (primary), 20F12, 18G30 (secondary).


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