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On anticonformal automorphisms of Riemann
surfaces with nonembeddable square


Author: Antonio F. Costa
Journal: Proc. Amer. Math. Soc. 124 (1996), 601-605
MSC (1991): Primary 30F99
DOI: https://doi.org/10.1090/S0002-9939-96-03066-3
MathSciNet review: 1301491
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we present an example of an anticonformal automorphism whose square has prime order and is not embeddable. We prove that every embeddable automorphism of odd order of a compact Riemann surface is the square of an orientation-reversing self-homeomorphism. Finally we study whether a conformal involution is the square of an orientation-reversing automorphism.


References [Enhancements On Off] (What's this?)

  • BC E. Bujalance and A. F. Costa, Orientation reversing automorphisms of Riemann surfaces, Illinois J. Math. 38 (1994), 616--623. CMP 94:14
  • BCF E. Bujalance, A. F. Costa, and A. Fernández, Uniformization of Klein surfaces by maximal NEC groups, Rev. Roumaine Math. Pures Appl. 40 (1995), 39--54.
  • G A. M. Garsia, An embedding of closed Riemann surfaces in Euclidean space, Comment. Math. Helv. 35 (1961), 93--110. MR 23:A2890
  • GM N. Greenleaf and C. L. May, Bordered Klein surfaces with maximal symmetry, Trans. Amer. Math. Soc. 274 (1982), 265--283. MR 84f:14022
  • M A. M. Macbeath, The classification of non-euclidean crystallographic groups, Canad. J. Math. 19 (1967), 1192--1205. MR 36:3890
  • N J. Nielsen, Die Struktur periodischer Transformationen von Flächen, Danske Vid Selsk.
    Mat-Fys. Medd. 1 (1937), 1--77.
  • R1 R.A. Rüedy, Embeddings of open Riemann surfaces, Comment. Math. Helv. 46 (1971), 214--225. MR 46:3781
  • R2 ------, Symmetric embeddings of Riemann surfaces, Princeton Univ. Press, Princeton, NJ, 1971, pp. 406--418. MR 52:3512
  • S D. Singerman, Symmetries and pseudosymmetries of hyperbolic surfaces, Glasgow Math. J. 21 (1980), 39--49. MR 81c:30080
  • Y K. Yocoyama, Complete classification of periodic maps on compact surfaces, Tokyo J. Math. 15 (1992), 247--279.
  • Z1 R. Zarrow, Anticonformal automorphisms of compact Riemann surfaces, Proc. Amer. Math. Soc. 54 (1976), 162--164. MR 53:8412
  • Z2 ------, Orientation reversing maps of surfaces, Illinois J. Math. 23 (1979), 82--92. MR 80k:57003b
  • Z3 ------, A counting function for orientation reversing maps, Illinois J. Math. 24 (1980), 469--476. MR 81f:58014

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Additional Information

Antonio F. Costa
Email: antonio.costa@uned.es

DOI: https://doi.org/10.1090/S0002-9939-96-03066-3
Received by editor(s): December 30, 1993
Received by editor(s) in revised form: April 29, 1994, and September 16, 1994
Additional Notes: The author was partially supported by DGICYT PB 92-0716 and EU project CHRX-CT93-408.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1996 American Mathematical Society

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