中文

Braid pictures for Artin groups

几何拓扑 2007-05-23 v1 群论

摘要

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 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.

关键词

引用

@article{arxiv.math/9907194,
  title  = {Braid pictures for Artin groups},
  author = {Daniel Allcock},
  journal= {arXiv preprint arXiv:math/9907194},
  year   = {2007}
}

备注

23 pages; 27 figures; submitted