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2010 Studying uniform thickness I: Legendrian simple iterated torus knots
Douglas J LaFountain
Algebr. Geom. Topol. 10(2): 891-916 (2010). DOI: 10.2140/agt.2010.10.891


We prove that the class of topological knot types that are both Legendrian simple and satisfy the uniform thickness property (UTP) is closed under cabling. An immediate application is that all iterated cabling knot types that begin with negative torus knots are Legendrian simple. We also examine, for arbitrary numbers of iterations, iterated cablings that begin with positive torus knots, and establish the Legendrian simplicity of large classes of these knot types, many of which also satisfy the UTP. In so doing we obtain new necessary conditions for both the failure of the UTP and Legendrian nonsimplicity in the class of iterated torus knots, including specific conditions on knot types.


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Douglas J LaFountain. "Studying uniform thickness I: Legendrian simple iterated torus knots." Algebr. Geom. Topol. 10 (2) 891 - 916, 2010.


Received: 12 June 2009; Revised: 17 December 2009; Accepted: 4 March 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1202.57009
MathSciNet: MR2629769
Digital Object Identifier: 10.2140/agt.2010.10.891

Primary: 57M25, 57R17
Secondary: 57M50

Rights: Copyright © 2010 Mathematical Sciences Publishers


Vol.10 • No. 2 • 2010
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