The Infimum, Supremum, and Geodesic Length of a Braid Conjugacy Class

✍ Scribed by Joan S. Birman; Ki Hyoung Ko; Sang Jin Lee

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 154 KB
• Volume: 164
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.2001.2010

✦ Synopsis

Algorithmic solutions to the conjugacy problem in the braid groups B n , n=2, 3, 4, ... were given in earlier work. This note concerns the computation of two integer class invariants, known as ''inf'' and ''sup.'' A key issue in both algorithms is the number m of times one must ''cycle'' (resp. ''decycle'') in order to either increase inf (resp. decrease sup) or to be sure that it is already maximal (resp. minimal) for the class. Our main result is to prove that m is bounded above by ((n 2 -n)/2) -1 in the situation stated by E. A.