Incompressible surfaces and (1,2)-knots

Mario Eudave-Munoz

doi:10.2140/gtm.2007.12.35

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arXiv · math/0703132

Incompressible surfaces and (1,2)-knots

Mario Eudave-Munoz

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Abstract

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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Mario Eudave-Munoz. 2009-03-30. Incompressible surfaces and (1,2)-knots. https://doi.org/10.2140/gtm.2007.12.35

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