English

Incompressible surfaces and (1,2)-knots

Geometric Topology 2009-03-30 v3

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.

Keywords

Cite

@article{arxiv.math/0703132,
  title  = {Incompressible surfaces and (1,2)-knots},
  author = {Mario Eudave-Munoz},
  journal= {arXiv preprint arXiv:math/0703132},
  year   = {2009}
}

Comments

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

R2 v1 2026-07-22T17:52:12.051Z