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On purely non-free finite actions of abelian groups on compact surfaces

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Abstract

A finite group of self-homeomorphisms of a closed orientable surface is said to act on it purely non-freely if each of its elements has a fixed point; we also call it a gpnf-action. In this paper we observe that gpnf-actions exist for an arbitrary finite group and we discuss the minimum genus problem for such actions. We solve it for abelian groups. In the cyclic case we prove that the minimal gpnf-action genus coincides with Harvey’s minimal genus.

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Authors and Affiliations

  1. Faculty of Computer Science, Białystok University of Technology, Białystok, Poland

    Czesław Bagiński

  2. Faculty of Mathematics, Physics and Informatics, Gdańsk University, Gdańsk, Poland

    Grzegorz Gromadzki

  3. Departamento de Matematica y Estadistica, Universidad de La Frontera, Temuco, Chile

    Ruben A. Hidalgo

Authors
  1. Czesław Bagiński
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  2. Grzegorz Gromadzki
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  3. Ruben A. Hidalgo
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Corresponding author

Correspondence to Grzegorz Gromadzki.

Additional information

C. Bagiński and G. Gromadzki are supported by Polish NCN 2015/17/B/ST1/03235, R. A. Hidalgo is supported by FONDECYT 1150003 and Anillo ACT 1415 PIA-CONICYT.

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Bagiński, C., Gromadzki, G. & Hidalgo, R.A. On purely non-free finite actions of abelian groups on compact surfaces. Arch. Math. 109, 311–321 (2017). https://doi.org/10.1007/s00013-017-1068-6

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  • DOI: https://doi.org/10.1007/s00013-017-1068-6

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