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Braid pictures for Artin groups Daniel Allcock
 

Summary: Braid pictures for Artin groups
Daniel Allcock
Department of Mathematics, Harvard University, Cambridge, MA 02138
allcock@math.harvard.edu
http://www.math.harvard.edu/allcock
Abstract
We de ne the braid groups of a two-dimensional orbifold and introduce con-
ventions 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
aĆne diagrams ~
A n , ~
B n , ~
C n and ~
D n as subgroups of the braid groups of var-
ious 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
~

  

Source: Allcock, Daniel - Department of Mathematics, University of Texas at Austin

 

Collections: Mathematics