Studying uniform thickness II: Transversely nonsimple iterated torus knots

LaFountain, Douglas

doi:10.2140/agt.2011.11.2741

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Studying uniform thickness II: Transversely nonsimple iterated torus knots

Douglas J LaFountain

Algebraic & Geometric Topology 11 (2011) 2741–2774

DOI: 10.2140/agt.2011.11.2741

Abstract

We prove that an iterated torus knot type in $(S^{3}, ξ_{std})$ 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

Volume 11, issue 5 (2011)