Generating pairs of 2-bridge knot groups

Details Generating pairs of 2-bridge knot groups Generating pairs of 2-bridge knot groups

2009-02-04

arxiv.org/abs/0902.0799v3

Mathematics

Geometric Topology

Final version to appear in Geometriae Dedicata

Scientific paper

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.

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