2002/06/26 by Joan S. Birman, Birman, Joan S., John Atwell Moody +2
Mathematics · Medicine · #20F36 #57M07 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Orthopedic Surgery and Rehabilitation #Shoulder and Clavicle Injuries #math.GR #math.GT #msc:20F36 #msc:57M07
paper · pdf · doi:10.48550/arxiv.math/0206283
31 pages, 6 figures. Revised to meet referee's comments. Accepted for publication in the Israel Journal of Mathematics
openalex publication_date 2002/06/26 · arxiv created 2003/10/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The recent proof by Bigelow and Krammer that the braid groups are linear opens the possibility of applications to the study of knots and links. It was proved by the first author and Menasco that any closed braid representative of the unknot can be systematically simplified to a round planar circle by a sequence of exchange moves and reducing moves. In this paper we establish connections between the faithfulness of the Krammer-Lawrence representation and the problem of recognizing when the conjugacy class of a closed braid admits an exchange move or a reducing move.