Configurations, braids, and homotopy groups

Berrick, A.; Cohen, F.; Wong, Y.; Wu, J.

doi:10.1090/S0894-0347-05-00507-2

Configurations, braids, and homotopy groups
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by A. J. Berrick, F. R. Cohen, Y. L. Wong and J. Wu

J. Amer. Math. Soc. 19 (2006), 265-326

DOI: https://doi.org/10.1090/S0894-0347-05-00507-2

Published electronically: November 18, 2005

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Abstract:

The main results of this article are certain connections between braid groups and the homotopy groups of the $2$-sphere. The connections are given in terms of Brunnian braids over the disk and over the $2$-sphere. The techniques arise from the natural structure of simplicial and $\Delta$-structures on fundamental groups of configuration spaces.

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