Nielsen Equivalence in Fuchsian groups

Martin Lustig; Yoav Moriah

doi:10.2140/agt.2022.22.189

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arXiv · 1910.02759

Nielsen Equivalence in Fuchsian groups

Martin Lustig·Yoav Moriah

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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.

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Martin Lustig, Yoav Moriah. 2019-10-07. Nielsen Equivalence in Fuchsian groups. https://doi.org/10.2140/agt.2022.22.189

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