The wellordering on positive braids

✍ Scribed by Serge Burckel

• Book ID: 104152839
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 969 KB
• Volume: 120
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(96)00072-2

✦ Synopsis

This paper studies Artin's braid monoids using combinatorial methods. More precisely, we investigate the linear ordering defined by Dehomoy. Laver has proved that the restriction of this ordering to positive braids is a wellordering. In order to study this order, we develop a natural wellordering < on the free monoid on infinitely many generators by representing words as trees. Our construction leads to a (new) normal form for (positive) braids. Our main result is that the restriction of our order << to the normal braid words coincides with the restriction of Dehomoy's ordering to positive braids. Our method gives an alternative proof of Laver's result using purely combinatorial arguments and gives the order type, namely wow.