2026-06-29T09:28:27Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/422132023-08-26T12:23:28Zcom_20.500.14352_14col_20.500.14352_15

Structure of Whittaker groups and applications to conformal involutions on handlebodies Díaz Sánchez, Raquel Garijo, Ignacio Hidalgo, Rubén A. Gromadzki, G. 514 Group actions in low dimensions Fuchsian groups and their generalizations Geometría 1204 Geometría 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. MEC, DGI Polish Ministry of Sciences and Higher Education Projects Fondecyt Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T00:12:59Z 2023-06-20T00:12:59Z 2010 journal article https://hdl.handle.net/20.500.14352/42213 0166-8641 10.1016/j.topol.2010.07.001 eng MTM 2006-14688 NN 201 366436 Fondecyt 1070271 UTFSM 12.09.02 restricted access application/pdf Elsevier Science