Braid pictures for Artin groups
Abstract
We define the braid groups of a twodimensional 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 tilde{A}_n, tilde{B}_n, tilde{C}_n and tilde{D}_n as subgroups of the braid groups of various simple orbifolds. The cases D_n, tilde{B}_n, tilde{C}_n and tilde{D}_n are new. In each case the Artin group is a normal subgroup with abelian quotient; in all cases except tilde{A}_n the quotient is finite. We illustrate the value of our braid calculus by performing with pictures a nontrivial calculation in the Artin groups of type D_n.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 1999
 arXiv:
 arXiv:math/9907194
 Bibcode:
 1999math......7194A
 Keywords:

 Geometric Topology;
 Group Theory;
 20F36
 EPrint:
 23 pages