Generating pairs of 2-bridge knot groups
Geometric Topology
2010-06-01 v3 Group Theory
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.
Keywords
Cite
@article{arxiv.0902.0799,
title = {Generating pairs of 2-bridge knot groups},
author = {Michael Heusener and Richard Weidmann},
journal= {arXiv preprint arXiv:0902.0799},
year = {2010}
}
Comments
Final version to appear in Geometriae Dedicata