Incompressible surfaces and (1,2)-knots

Details Incompressible surfaces and (1,2)-knots Incompressible surfaces and (1,2)-knots

2007-03-05

arxiv.org/abs/math/0703132v3

Geom. Topol. Monogr. 12 (2007) 35-87

Mathematics

Geometric Topology

This is the version published by Geometry & Topology Monographs on 3 December 2007

Scientific paper

10.2140/gtm.2007.12.35

We give a description of all (1,2)-knots in S^3 which admit a closed meridionally incompressible surface of genus 2 in their complement. That is, we give several constructions of (1,2)-knots having a meridionally incompressible surface of genus 2, and then show that any such surface for a (1,2)-knot must come from one of the constructions. As an application, we show explicit examples of tunnel number one knots which are not (1,2)-knots.

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