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2011 Studying uniform thickness II: Transversely nonsimple iterated torus knots
Douglas LaFountain
Algebr. Geom. Topol. 11(5): 2741-2774 (2011). DOI: 10.2140/agt.2011.11.2741

Abstract

We prove that an iterated torus knot type in (S3,ξstd) fails the uniform thickness property (UTP) if and only if it is formed from repeated positive cablings, which is precisely when an iterated torus knot supports the standard contact structure. This is the first complete UTP classification for a large class of knots. We also show that all iterated torus knots that fail the UTP support cabling knot types that are transversely nonsimple.

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Douglas LaFountain. "Studying uniform thickness II: Transversely nonsimple iterated torus knots." Algebr. Geom. Topol. 11 (5) 2741 - 2774, 2011. https://doi.org/10.2140/agt.2011.11.2741

Information

Received: 14 April 2011; Revised: 3 September 2011; Accepted: 4 September 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1271.57022
MathSciNet: MR2846910
Digital Object Identifier: 10.2140/agt.2011.11.2741

Subjects:
Primary: 57M25, 57R17
Secondary: 57M50

Rights: Copyright © 2011 Mathematical Sciences Publishers

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Vol.11 • No. 5 • 2011
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