Generating pairs of 2-bridge knot groups

2009/02/04 by Michael Heusener, Richard Weidmann, Heusener, Michael +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · doi:10.48550/arxiv.0902.0799

openalex publication_date 2009/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Nielsen equivalence classes of generating pairs of Kleinian groups and HNN-extensions. We establish the following facts: - Hyperbolic 2-bridge knot groups have infinitely many Nielsen classes of generating pairs. - For any natural number N there is a closed hyperbolic 3-manifold whose fundamental group has N distinct Nielsen classes of generating pairs. - Two pairs of elements of a fundamental group of an HNN-extension are Nielsen equivalent iff they are so for the obvious reasons.

Related

• Parabolic generating pairs of genus-one 2-bridge knot groups
• Classification of parabolic generating pairs of Kleinian groups with two parabolic generators
• Determining knot groups by finite quotients
• Generating function on epimorphisms between 2-bridge knot groups
• Two-parabolic-generator subgroups of hyperbolic 3-manifold groups