caa a22 4500 445884347 CHVBK 20180317145554.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10711-010-9534-3 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9534-3 Generating pairs of 2-bridge knot groups [Elektronische Daten] [Michael Heusener, Richard Weidmann] We study Nielsen equivalence classes of generating pairs of Kleinian groups and HNN-extensions. We establish the following facts: (1)Hyperbolic 2-bridge knot groups have infinitely many Nielsen classes of generating pairs.(2)For any $${n\in\mathbb{N}}$$ there is a closed hyperbolic 3-manifold whose fundamental group has n distinct Nielsen classes of generating pairs.(3)Two pairs of elements of a fundamental group of an HNN-extension are Nielsen equivalent iff they are so for the obvious reasons. Springer Science+Business Media B.V., 2010 2-bridge knot nationallicence Fundamental group nationallicence Nielsen equivalence nationallicence Heusener Michael Clermont Université, Université Blaise Pascal et CNRS, Laboratoire de Mathématiques, BP 10448, 63000, Clermont-Ferrand, France aut Weidmann Richard Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn Str. 4, 24098, Kiel, Germany aut Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 279-295 0046-5755 151:1<279 2011 151 10711 https://doi.org/10.1007/s10711-010-9534-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9534-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Heusener Michael Clermont Université, Université Blaise Pascal et CNRS, Laboratoire de Mathématiques, BP 10448, 63000, Clermont-Ferrand, France aut NATIONALLICENCE 700 1- Weidmann Richard Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn Str. 4, 24098, Kiel, Germany aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 279-295 0046-5755 151:1<279 2011 151 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer