Generalizations of hyperbolic area for topological surfaces

• Aldo Hilario Cruz Cota ^[1]
  1. [1] Texas Wesleyan University

     Texas Wesleyan University

     Estados Unidos

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 59, Nº. 2, 2018, págs. 431-441
• Idioma: inglés
• DOI: 10.33044/revuma.v59n2a11
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• Resumen

  • We introduce two generalizations of hyperbolic area for connected, closed, orientable surfaces: the complexity and the simple complexity of a surface. These concepts are defined in terms of collections of branched coverings M→P1, where M is a Riemann surface homeomorphic to S and P1 is the Riemann sphere. We prove that if S is a surface of positive genus, then both the topological complexity and the simple topological complexity of S are linear functions of its genus.