%0 Journal Article
%A Díaz Sánchez, Raquel
%A Garijo, Ignacio
%A Hidalgo, Rubén A.
%A Gromadzki, G.
%T Structure of Whittaker groups and applications to conformal involutions on handlebodies
%D 2010
%@ 0166-8641
%U https://hdl.handle.net/20.500.14352/42213
%X 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.
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