Obstructions to trivializing a knot
Geometric Topology
2007-05-23 v2 Group Theory
Abstract
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.
Keywords
Cite
@article{arxiv.math/0206283,
title = {Obstructions to trivializing a knot},
author = {Joan S. Birman and John A. Moody},
journal= {arXiv preprint arXiv:math/0206283},
year = {2007}
}
Comments
31 pages, 6 figures. Revised to meet referee's comments. Accepted for publication in the Israel Journal of Mathematics