Abstract
We define the braid groups of a two-dimensional orbifold and introduce conventions for drawing braid pictures. We use these to realize the Artin groups associated to the spherical Coxeter diagrams A n , B n = C n and D n and the affine diagrams A n , B n , C n and D n as subgroups of the braid groups of various simple orbifolds. The cases D n , B n , C n and D n are new. In each case the Artin group is a normal subgroup with abelian quotient; in all cases except A n the quotient is finite. We also illustrate the value of our braid calculus by giving a picture-proof of the basic properties of the Garside element of an Artin group of type D n .
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