Geometry & Topology Monographs 12 (2007) 35–87

DOI: 10.2140/gtm.2007.12.35

arXiv: math.GT/0703132

Abstract

We give a description of all (1,2)–knots in S³ 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.

Keywords

(1,2)–knot, meridionally incompressible surface, tunnel number one knot

Mathematical Subject Classification

Primary: 57M25

Secondary: 57N10

References

Publication

Received: 4 October 2006
Revised: 7 February 2007
Accepted: 6 April 2007
Published: 3 December 2007

Authors