1999/07/30 by Daniel Allcock, Allcock, Daniel · 4 citations
Mathematics · #20F36 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #math.GT #msc:20F36
paper · pdf · doi:10.48550/arxiv.math/9907194
23 pages; 27 figures; submitted
arxiv created 1999/07/30 · openalex publication_date 1999/07/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 An, Bn=Cn and Dn and the affine diagrams tildeAn, tildeBn, tildeCn and tildeDn as subgroups of the braid groups of various simple orbifolds. The cases Dn, tildeBn, tildeCn and tildeDn are new. In each case the Artin group is a normal subgroup with abelian quotient; in all cases except tildeAn 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 Dn.