Nielsen Equivalence in Fuchsian groups

DOI10.2140/AGT.2022.22.189arXiv1910.02759MaRDI QIDQ6326668

Publication date: 7 October 2019

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.

Mathematics Subject Classification ID

General low-dimensional topology (57M99) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10)

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