Nielsen Equivalence in Fuchsian groups

Abstract

In this paper we give a complete classification of minimal generating systems in a very general class of Fuchsian groups G. This class includes for example any G which has at least seven non-conjugate cyclic subgroups of order greater than 2. In particular, the well known problematic cases where G has characteristic exponents equal to 2 are not excluded. We classify generating systems up to Nielsen equivalence; this notion is strongly related to Heegaard splittings of 3-manifolds. The results of this paper provide in particular the tools for a rather general extension of previous work of the authors and others, on the isotopy classification of such splittings in Seifert fibered spaces.

26 pqges No Figures, Minor corrections

References in corpus (7)

• Dynamics of Aut(Fn) Actions on Group Presentations and Representations
• Nielsen equivalence in closed surface groups
• Nielsen equivalence and trisections of 4-manifolds
• Nielsen equivalence in a class of random groups
• Nielsen equivalence in closed 2-orbifold groups
• Interactions of Computational Complexity Theory and Mathematics
• Irreducible generating tuples of Fuchsian groups