Title: A GEOMETRIC AND ALGEBRAIC DESCRIPTION OF ANNULAR BRAID GROUPS
Abstract: We provide a new presentation for the annular braid group. The annular braid group is known to be isomorphic to the finite type Artin group with Coxeter graph B n . Using our presentation, we show that the annular braid group is a semidirect product of an infinite cyclic group and the affine Artin group with Coxeter graph à n - 1 . This provides a new example of an infinite type Artin group which injects into a finite type Artin group. In fact, we show that the affine braid group with Coxeter graph à n - 1 injects into the braid group on n + 1 stings. Recently it has been shown that the braid groups are linear, see [3]. Therefore, this shows that the affine braid groups are also linear.
Publication Year: 2002
Publication Date: 2002-02-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 58
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot