Algorithmically detecting the bridge number of hyperbolic knots

2007/10/05 by Alexander Coward, Coward, Alexander
Computer Science · Mathematics · #57M25 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0710.1262

openalex publication_date 2007/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We exhibit an algorithm to determine the bridge number of a hyperbolic knot in the 3-sphere. The proof uses adaptations of almost normal surface theory for compact surfaces with boundary in ideally triangulated knot exteriors.

Related

• Bridge numbers and meridional ranks of knotted surfaces and welded knots
• Genus bounds bridge number for high distance knots
• Hyperbolic Knot Theory
• Determining knot groups by finite quotients
• Geodesic surfaces in the complement of knots with small crossing number