Classification of alternating knots with tunnel number one

2001/03/30 by Marc Lackenby, Lackenby, Marc
Computer Science · Mathematics · #57M25 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M25 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0103217

38 pages, 26 figures; to appear in Communications in Analysis and Geometry

openalex publication_date 2001/03/30 · arxiv created 2002/08/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper gives a complete classification of all alternating knots with tunnel number one, and all their unknotting tunnels. We prove that the only such knots are two-bridge knots and certain Montesinos knots.

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