Braid pictures for Artin groups

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dc.creatorAllcock, Daniel
dc.date1999-07-30
dc.date.accessioned2026-07-07T05:30:08Z
dc.date.available2026-07-07T05:30:08Z
dc.descriptionWe 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 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.
dc.description23 pages; 27 figures; submitted
dc.identifierhttps://arxiv.org/abs/math/9907194
dc.identifierhttp://arxiv.org/abs/math/9907194
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78897
dc.subjectGeometric Topology
dc.subjectGroup Theory
dc.subject20F36
dc.titleBraid pictures for Artin groups
dc.typetext

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