Generating pairs of 2-bridge knot groups

Michael Heusener (1) , Richard Weidmann (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 Mathematisches Seminar [Kiel]

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.

Mots clés: hyperbolic 3-manifolds; Nielsen equivalence classes of generating pairs

Domaines: Topologie géométrique [math.GT]; Théorie des groupes [math.GR]

Michael Heusener, Richard Weidmann. Generating pairs of 2-bridge knot groups. Geometriae Dedicata, 2010, 151 (1), pp.279-295. ⟨10.1007/s10711-010-9534-3⟩. ⟨hal-00358607v3⟩