A note on the homology covering of closed Klein surfaces

• Hidalgo, Rubén ^[1]
  1. [1] Universidad Técnica Federico Santa María.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 18, Nº. 2, 1999, págs. 165-173
• Idioma: inglés
• DOI: 10.22199/S07160917.1999.0002.00004
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• Resumen

  • In previous works we have seen that a finitely generated torsion-free non-elementary function group is uniquely determined by its commutator subgroup. In this note, we observe that under the presence of orientation-reversing conformal automorphisms the above rigidity property still valid. More precisely, we see that finitely generated torsion-free reversing Fuchsian groups of the first kind, without parabolic transformations, are uniquely determined by their commutator subgroup. The arguments of the proof follows the same lines as for the orientable situation.

• Referencias bibliográficas
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  • [2] R.A. Hidalgo. Homology coverings of Riemann surfaces. Tôhoku Math. J. 45, pp. 499-503, (1993).
  • [3] . A commutator rigidity for function groups. Preprint.
  • [4] B. Maskit. The Homology Covering of a Riemann Surface. Tôhoku Math. J. 38, pp. 561-562, (1986).
  • [5] . On boundaries of Teichmüller spaces and kleinian groups II. Ann. Of Math. 91, PP. 607-639, (1970).