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Lifting a symmetry of a Riemann surface

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

Let X be a compact Riemann surface of genus \(g \ge 2\) that possesses a fixed point free group H of automorphisms and let \(Y=X/H\) denote the orbit space of X under the action of H. Assume Y possesses a symmetry \(\sigma ,\) that is, an anticonformal involution. We give conditions that determine when \(\sigma \) lifts to an anticonformal automorphism of the surface X. The study splits naturally into three cases according to the different topological types that \(\sigma \) may possess. We apply the criterion to abelian groups and also to particular presentations of other types of groups.

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Acknowledgements

The authors wish to thank the careful referees for their suggestions and comments which have contributed to get a more readable paper.

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Authors and Affiliations

  1. Universidad Nacional de Educacion a Distancia, Madrid, Spain

    Emilio Bujalance & Francisco-Javier Cirre

  2. Purdue University Northwest, Indiana, USA

    Peter Turbek

Authors
  1. Emilio Bujalance
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  2. Francisco-Javier Cirre
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  3. Peter Turbek
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Corresponding author

Correspondence to Francisco-Javier Cirre.

Additional information

F. J. Cirre and E. Bujalance: Partially supported by Project MTM2014-55812.

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Bujalance, E., Cirre, FJ. & Turbek, P. Lifting a symmetry of a Riemann surface. RACSAM 112, 767–779 (2018). https://doi.org/10.1007/s13398-017-0475-7

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  • DOI: https://doi.org/10.1007/s13398-017-0475-7

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