Díaz Sánchez, RaquelGarijo, IgnacioHidalgo, Rubén A.Gromadzki, G.2023-06-202023-06-2020100166-864110.1016/j.topol.2010.07.001https://hdl.handle.net/20.500.14352/42213The 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.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0166864110001987http://www.sciencedirect.com/restricted access514Group actions in low dimensionsFuchsian groups and their generalizationsGeometría1204 Geometría