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Structure of Whittaker groups and applications to conformal involutions on handlebodies

Díaz Sánchez, Raquel and Garijo, Ignacio and Hidalgo, Rubén A. and 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.

Item Type:Article
Uncontrolled Keywords:Group actions in low dimensions; Fuchsian groups and their generalizations
Subjects:Sciences > Mathematics > Geometry
ID Code:15716

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