On tunnel number one knots that are not (1,n)

2006/06/09 by Jesse Johnson, Johnson, Jesse, Abigail Thompson +1
Computer Science · Mathematics · #57M #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0606226

7 pages

openalex publication_date 2006/06/09 · arxiv created 2007/01/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the bridge number of a t bridge knot in S³ with respect to an unknotted genus t surface is bounded below by a function of the distance of the Heegaard splitting induced by the t bridges. It follows that for any natural number n, there is a tunnel number one knot in S³ that is not (1,n).

Related

• Genus two Heegaard splittings of exteriors of 1-genus 1-bridge knots II
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• Genus two Heegaard splittings of exteriors of 1-genus 1-bridge knots
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• Iterated splitting and the classification of knot tunnels