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Journal of the London Mathematical Society Advance Access published online on September 28, 2007
Journal of the London Mathematical Society, doi:10.1112/jlms/jdm049
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© 2007 London Mathematical Society

The Braid Group of Zn

Daan Krammer

Department of Mathematics
University of Warwick
Coventry CV4 7AL
United Kingdom

We define pseudo-Garside groups and prove a theorem parallel to Garside's result on the word problem for the usual braid groups. The main novelty is that the set of simple elements can be infinite. A group B = B(Zn) called the braid group of Zn and which resembles mapping class groups is introduced. It is to GL(n,Z) what the braid group is to the symmetric group Sn. We prove that B is a pseudo-Garside group. We give a small presentation for B(Zn) assuming one for B(Z3) is given.

2000 Mathematics Subject Classification 20F60 (primary), 06F15, 20F05, 20F36, 20H05 (secondary).

Received March 2, 2006; revised February 16, 2007;
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