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2001 On iterated torus knots and transversal knots
William W Menasco
Geom. Topol. 5(2): 651-682 (2001). DOI: 10.2140/gt.2001.5.651


A knot type is exchange reducible if an arbitrary closed n–braid representative K of K can be changed to a closed braid of minimum braid index nmin(K) by a finite sequence of braid isotopies, exchange moves and ±–destabilizations. In a preprint of Birman and Wrinkle, a transversal knot in the standard contact structure for S3 is defined to be transversally simple if it is characterized up to transversal isotopy by its topological knot type and its self-linking number. Theorem 2 in the preprint establishes that exchange reducibility implies transversally simplicity. The main result in this note, establishes that iterated torus knots are exchange reducible. It then follows as a corollary that iterated torus knots are transversally simple.


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William W Menasco. "On iterated torus knots and transversal knots." Geom. Topol. 5 (2) 651 - 682, 2001.


Received: 27 March 2001; Revised: 17 July 2001; Accepted: 15 August 2001; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 1002.57025
MathSciNet: MR1857523
Digital Object Identifier: 10.2140/gt.2001.5.651

Primary: 57M27 , 57N16 , 57R17
Secondary: 37F20

Keywords: braids , cabling , contact structures , exchange reducibility , torus knots

Rights: Copyright © 2001 Mathematical Sciences Publishers


Vol.5 • No. 2 • 2001
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