Generating pairs of 2-bridge knot groups

Michael Heusener; Richard Weidmann

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arXiv · 0902.0799

Generating pairs of 2-bridge knot groups

Michael Heusener·Richard Weidmann

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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.

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Michael Heusener, Richard Weidmann. 2009-02-04. Generating pairs of 2-bridge knot groups. https://arxiv.org/abs/0902.0799

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