Studying uniform thickness II: Transversely non-simple iterated torus knots

Details Studying uniform thickness II: Transversely non-simple iterated torus knots Studying uniform thickness II: Transversely non-simple iterated torus knots

2009-09-08

arxiv.org/abs/0909.1452v2

Mathematics

Geometric Topology

26 pages, 3 figures. Old section 4 is removed, and corrected in arXiv:1104.0550; revised to reflect these changes

Scientific paper

We prove that an iterated torus knot type fails the uniform thickness
property (UTP) if and only if all of its iterations are positive cablings,
which is precisely when an iterated torus knot type supports the standard
contact structure. We also show that all iterated torus knots that fail the UTP
support cabling knot types that are transversely non-simple.

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