Simon's conjecture for 2-bridge knots

2009/03/17 by Michel Boileau, Boileau, Michel, Steve Boyer +5 · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0903.2898

openalex publication_date 2009/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is conjectured that for each knot K in S³, the fundamental group of its complement surjects onto only finitely many distinct knot groups. Applying character variety theory we obtain an affirmative solution of the conjecture for a class of small knots that includes 2-bridge knots.

Citations

• Dehn Surgery on Knots

Cited by

• Simon's conjecture for fibered knots
• Knot Groups with Many Killers
• More Exotic \mathbbRP²-knots and Homotopy Spheres

Related

• Finiteness of a section of the SL(2,ℂ)-character variety of knot groups
• The 2-bridge knots of up to 16 crossings
• Determining knot groups by finite quotients
• Unsolvable problems about higher-dimensional knots and related groups
• Farey recursion and the character varieties for 2-bridge knots