Israel Journal of Mathematics

, Volume 142, Issue 1, pp 125–162 | Cite as

Obstructions to trivializing a knot

  • Joan S. Birman
  • John Atwell Moody


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 finite 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.


Intersection Pairing Conjugacy Class Homotopy Class Homology Class Braid Group 
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Copyright information

© Hebrew University 2004

Authors and Affiliations

  1. 1.Department of MathematicsColumbia UniversityNew YorkUSA
  2. 2.Mathematics InstituteUniversity of WarwickCoventryEngland

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