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There are no unexpected tunnel number one knots of genus one

2001/06/04 by Martin Scharlemann, Scharlemann, Martin
Computer Science · Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M25 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0106017

73 pp. including 30 figures

arxiv created 2001/06/04 · openalex publication_date 2001/06/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The only knots that are tunnel number one and genus one are those that are already known: 2-bridge knots obtained by plumbing together two unknotted annuli and the satellite examples classified by Eudave-Munoz and by Morimoto-Sakuma. This confirms a conjecture first made by Goda and Teragaito.

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