Geodesic
Studying uniform thickness II: Transversely nonsimple iterated torus knots
LaFountain, Douglas1
1Centre for Quantum Geometry of Moduli Spaces, Aarhus University, Ny Munkegade 118, DK-8000 Aarhus C, Denmark
Algebraic and Geometric Topology, Tome 11 (2011) no. 5, pp. 2741-2774
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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.

DOI : 10.2140/agt.2011.11.2741
Classification : 57M25, 57R17, 57M50
Keywords: uniform thickness property, transverse knot, convex surface

LaFountain, Douglas  1

1 Centre for Quantum Geometry of Moduli Spaces, Aarhus University, Ny Munkegade 118, DK-8000 Aarhus C, Denmark 
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LaFountain, Douglas. Studying uniform thickness II: Transversely nonsimple iterated torus knots. Algebraic and Geometric Topology, Tome 11 (2011) no. 5, pp. 2741-2774. doi: 10.2140/agt.2011.11.2741

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