Algorithmically detecting the bridge number of hyperbolic knots

2007/10/05 by Alexander Coward, Coward, Alexander · 1 citation
Computer Science · Mathematics · #57M25 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M25 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0710.1262

42 pages, 23 figures; v2 contains a rewritten introduction and updated references

openalex publication_date 2007/10/05 · arxiv created 2012/03/27 · arxiv updated 2012/03/29 · 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.

Cited by

• Heegaard structure respects complicated JSJ decompositions

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