Extensions of finite cyclic group actions on bordered surfaces

• Emilio Bujalance ^[1] ; Francisco Javier Cirre ^[1] ; Marston D. E. Conder ^[2]
  1. [1] Universidad Nacional de Educación a Distancia

     Universidad Nacional de Educación a Distancia

     Madrid, España

     
  2. [2] University of Auckland

     University of Auckland

     Nueva Zelanda

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, Nº 1, 2015, págs. 349-372
• Idioma: inglés
• DOI: 10.4171/RMI/837
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study the question of the extendability of the action of a finite cyclic group on a compact bordered Klein surface (either orientable or non-orientable). This extends previous work by the authors for group actions on unbordered surfaces. It is shown that if such a cyclic action is realised by means of a non-maximal NEC signature, then the action always extends. For a given integer g≥2, we determine the order of the largest cyclic group that acts as the full automorphism group of a bordered surface of algebraic genus g, and the topological type of the surfaces on which the largest action takes place. In addition, we calculate the smallest algebraic genus of a bordered surface on which a given cyclic group acts as the full automorphism group of the surface. For this, we deal separately with orientable and non-orientable surfaces, and we also determine the topological type of the surfaces attaining the bounds.