Boundary slope diameter and crossing number of 2-bridge knots

2005/10/24 by Thomas W. Mattman, Mattman, Thomas W., Gabriel Maybrun +3
Computer Science · Mathematics · #57M25 (Primary) #57M27 (secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M25 #msc:57M27 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0510496

21 pages, 7 figures. v2 - No changes - we only wish to note that this is an early version of a paper to appear in The Osaka Journal of Mathematics

openalex publication_date 2005/10/24 · arxiv created 2007/04/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for 2-bridge knots, the diameter, D, of the set of boundary slopes is twice the crossing number, c. This constitutes partial verification of a conjecture that, for all knots in S³, D is at most 2c.

Related

• Boundary slopes of 2-bridge links determine the crossing number
• Alternating knots with large boundary slope diameter
• Lower bounds on boundary slope diameters for Montesinos knots
• Repeated boundary slopes for 2-bridge knots
• Computing boundary slopes of 2-bridge links