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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Configurations, braids, and homotopy groups


Authors: A. J. Berrick, F. R. Cohen, Y. L. Wong and J. Wu
Journal: J. Amer. Math. Soc. 19 (2006), 265-326
MSC (2000): Primary 20F36, 55Q40, 55U10; Secondary 20F12, 20F14, 57M50
Published electronically: November 18, 2005
MathSciNet review: 2188127
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

A. J. Berrick
Affiliation: Department of Mathematics, National University of Singapore, Kent Ridge 117543, Singapore
Email: berrick@math.nus.edu.sg

F. R. Cohen
Affiliation: Department of Mathematics, University of Rochester, Rochester, New York 14627
Email: cohf@math.rochester.edu

Y. L. Wong
Affiliation: Department of Mathematics, National University of Singapore, Kent Ridge 117543, Singapore
Email: matwyl@nus.edu.sg

J. Wu
Affiliation: Department of Mathematics, National University of Singapore, Kent Ridge 117543, Singapore
Email: matwuj@nus.edu.sg

DOI: http://dx.doi.org/10.1090/S0894-0347-05-00507-2
PII: S 0894-0347(05)00507-2
Keywords: Braid group, Brunnian braid, configuration space, crossed simplicial group, Moore complex, homotopy groups of spheres
Received by editor(s): April 28, 2003
Published electronically: November 18, 2005
Additional Notes: Research of the first, third, and last authors is supported in part by the Academic Research Fund of the National University of Singapore R-146-000-048-112 and R-146-000-049-112.
The second author is partially supported by the US National Science Foundation grant DMS 0072173 and CNRS-NSF grant 17149
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.