Obstructions to trivializing a knot
Birman, J. S. and Moody, John Atwell. (2004) Obstructions to trivializing a knot. Israel Journal of Mathematics, Vol.142 (No.1). pp. 125-162. ISSN 0021-2172Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/BF02771530
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.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Israel Journal of Mathematics|
|Number of Pages:||38|
|Page Range:||pp. 125-162|
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