3 research outputs found
Nielsen Equivalence in Fuchsian groups
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.Comment: 26 pqges No Figures, Minor correction
International Congress of Mathematicians: 2022 July 6β14: Proceedings of the ICM 2022
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