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Structure of Whittaker groups and applications to conformal involutions on handlebodies


Díaz Sánchez, Raquel y Garijo, Ignacio y Hidalgo, Rubén A. y Gromadzki, G. (2010) Structure of Whittaker groups and applications to conformal involutions on handlebodies. Topology and its Applications, 157 (15). pp. 2347-2361. ISSN 0166-8641

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The geometrically finite complete hyperbolic Riemannian metrics in the interior of a handlebody of genus g, having injectivity radius bounded away from zero, are exactly those produced by Schottky groups of rank g; these are called Schottky structures. A Whittakergroup of rank g is by definition a Kleinian groupK containing, as an index two subgroup, a Schottky groupΓ of rank g. In this case, K corresponds exactly to a conformalinvolution on the handlebody with Schottky structure given by Γ. In this paper we provide a structural description of Whittakergroups and, as a consequence of this, we obtain some facts concerning conformalinvolutions on handlebodies. For instance, we give a formula to count the type and the number of connected components of the set of fixed points of a conformalinvolution of a handlebody with a Schottky structure in terms of a group of automorphisms containing the conformalinvolution.

Tipo de documento:Artículo
Palabras clave:Group actions in low dimensions; Fuchsian groups and their generalizations
Materias:Ciencias > Matemáticas > Geometría
Código ID:15716

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Última Modificación:06 Feb 2014 10:30

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