Volume 11, issue 5 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Studying uniform thickness II: Transversely nonsimple iterated torus knots

Douglas J LaFountain

Algebraic & Geometric Topology 11 (2011) 2741–2774
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.

Keywords
uniform thickness property, transverse knot, convex surface
Mathematical Subject Classification 2010
Primary: 57M25, 57R17
Secondary: 57M50
References
Publication
Received: 14 April 2011
Revised: 3 September 2011
Accepted: 4 September 2011
Published: 24 September 2011
Authors
Douglas J LaFountain
Centre for Quantum Geometry of Moduli Spaces
Aarhus University
Ny Munkegade 118
DK-8000 Aarhus C
Denmark