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On braid groups and homotopy groups

F R Cohen and Jie Wu

Geometry & Topology Monographs 13 (2008) 169–193

DOI: 10.2140/gtm.2008.13.169

arXiv: 0904.0783

Abstract

This article is an exposition of certain connections between the braid groups, classical homotopy groups of the 2–sphere, as well as Lie algebras attached to the descending central series of pure braid groups arising as Vassiliev invariants of pure braids. Natural related questions are posed at the end of this article.

Keywords

braid groups, simplicial groups, Brunnian braids, almost Brunnian braids, Vassiliev invariants, Cabling operation, Δ-groups

Mathematical Subject Classification

Primary: 20F36, 55Q40

Secondary: 18G30, 20F40, 55U10

References
Publication

Received: 11 July 2006
Revised: 29 May 2007
Accepted: 1 June 2007
Published: 22 February 2008

Authors
F R Cohen
Department of Mathematics
University of Rochester
Rochester, NY 14627
USA
http://www.math.rochester.edu/people/faculty/cohf/
Jie Wu
Department of Mathematics
National University of Singapore
Singapore 117543
Republic of Singapore
http://www.math.nus.edu.sg/~matwujie