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On the topological type of anticonformal square roots of automorphisms of Riemann surfaces

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Abstract

Let X be a compact Riemann surface and f be a conformal automorphism of X of order n. An anticonformal square root of f is an anticonformal automorphism g of X such that g2=f. If g1 and g2 are two anticonformal square roots of f we study the problem of whether g1 and g2 have the same topological type, i. e., if there exists a homeomorphism h:X→X such that g1=hg2h−1. We use techniques of noneuclidean crystallographic (NEC) groups and the topological classification of orientation reversing maps of finite period on surfaces given in [C1] and [Y].

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Authors and Affiliations

  1. Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, 28040, Madrid, Spain

    Antonio F. Costa

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  1. Antonio F. Costa
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Partially supported by DGICYT PB92-0716 and EC project CHRX-CT93-408

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Costa, A.F. On the topological type of anticonformal square roots of automorphisms of Riemann surfaces. Manuscripta Math 89, 87–102 (1996). https://doi.org/10.1007/BF02567507

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  • DOI: https://doi.org/10.1007/BF02567507

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