Obstructions to trivializing a knot

Details Obstructions to trivializing a knot Obstructions to trivializing a knot

2002-06-26

arxiv.org/abs/math/0206283v2

Mathematics

Geometric Topology

31 pages, 6 figures. Revised to meet referee's comments. Accepted for publication in the Israel Journal of Mathematics

Scientific paper

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.

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