Studying uniform thickness I: Legendrian simple iterated torus knots

Details Studying uniform thickness I: Legendrian simple iterated torus knots Studying uniform thickness I: Legendrian simple iterated torus knots

2009-05-17

arxiv.org/abs/0905.2760v3

Mathematics

Geometric Topology

21 pages, 5 figures; final version, to appear in Algebraic and Geometric Topology

Scientific paper

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 non-simplicity in the class of iterated torus knots, including specific conditions on knot types.

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