Título:
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Hyperelliptic Klein surfaces with maximal symmetry
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Autores:
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Bujalance, E. ;
Etayo Gordejuela, J. Javier
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Tipo de documento:
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texto impreso
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Editorial:
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Cambridge University Press, 1986
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Grupos (Matemáticas)
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Tipo = Sección de libro
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Resumen:
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A Klein surface S is a surface with a dianalytic structure. If S is compact then its underlying topological surface can be orientable or nonorientable and may have boundary. The genus of S is then defined to be the genus of its canonical double which becomes the complex double S ˆ of S when given the canonical complex structure. We call S hyperelliptic if S ˆ is a hyperelliptic Riemann surface. The automorphism group of a Klein surface of genus g is bounded above by 12(g?1) [N. Greenleaf and C. L. May , Trans. Amer. Math. Soc. 274 (1982), no. 1, 265--283]. In the present paper the authors prove that if S is a hyperelliptic Klein surface with 12(g?1) automorphisms then S is homeomorphic to a sphere with 3 holes or a torus with 1 hole. The subspace of Teichmüller space corresponding to these surfaces is briefly considered and shown to consist of submanifolds of dimension 1. The proofs use the algebraic structure of NEC groups.
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