The braid group of Z^n

Details The braid group of Z^n The braid group of Z^n

2006-03-16

arxiv.org/abs/math/0603399v2

Mathematics

Group Theory

minor changes, 21 pages, one figure and four diagrams made by pstricks, essentially final version

Scientific paper

We define pseudo-Garside groups and prove a theorem about them 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. We introduce a group B=B(Z^n) which we call the braid group of Z^n, and which bears some vague resemblance to mapping class groups. It is to GL(n,Z) what the braid group is to the symmetric group S_n. We prove that B is a pseudo-Garside group. We give a small presentation for B(Z^n) assuming one for B(Z^3) is given.

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