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Título:
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Uniformization of conformal involutions on stable Riemann surfaces
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Autores:
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Díaz Sánchez, Raquel ;
Garijo, Ignacio ;
Hidalgo, Rubén A.
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Tipo de documento:
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texto impreso
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Editorial:
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Hebrew University Magnes Press, 2011
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/restrictedAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Geometría
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Tipo = Artículo
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Resumen:
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Let S be a closed Riemann surface of genus g. It is well known that there are Schottky groups producing uniformizations of S (Retrosection Theorem). Moreover, if ?: S ? S is a conformal involution, it is also known that there is a Kleinian group K containing, as an index two subgroup, a Schottky group G that uniformizes S and so that K/G induces the cyclic group ???. Let us now assume S is a stable Riemann surface and ?: S ? S is a conformal involution. Again, it is known that S can be uniformized by a suitable noded Schottky group, but it is not known whether or not there is a Kleinian group K, containing a noded Schottky group G of index two, so that G uniformizes S and K/G induces ???. In this paper we discuss this existence problem and provide some partial answers: (1) a complete positive answer for genus g ? 2 and for the case that S/??? is of genus zero; (2) the existence of a Kleinian group K uniformizing the quotient stable Riemann orbifold S/???. Applications to handlebodies with orientation-preserving involutions are also provided.
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En línea:
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https://eprints.ucm.es/id/eprint/15719/1/DiazRaquel09.pdf
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