Studying uniform thickness I: Legendrian simple iterated torus knots

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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Keywords

Legendrian knots, convex surfaces, uniform thickness property

Mathematical Subject Classification 2000

Primary: 57M25, 57R17

Secondary: 57M50

References

Publication

Received: 12 June 2009

Revised: 17 December 2009

Accepted: 4 March 2010

Published: 13 April 2010

Authors

Douglas J LaFountain
Department of Mathematics University at Buffalo 244 Mathematics Building Buffalo, NY 14260 USA

Volume 10, issue 2 (2010)

Douglas J LaFountain

Abstract