RT Journal Article
T1 Structure of Whittaker groups and applications to conformal involutions on handlebodies
A1 Díaz Sánchez, Raquel
A1 Garijo, Ignacio
A1 Hidalgo, Rubén A.
A1 Gromadzki, G.
AB 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.
PB Elsevier Science
SN 0166-8641
YR 2010
FD 2010
LK https://hdl.handle.net/20.500.14352/42213
UL https://hdl.handle.net/20.500.14352/42213
LA eng
NO MEC, DGI
NO Polish Ministry of Sciences and Higher Education
NO Projects Fondecyt
DS Docta Complutense
RD 20 jul 2025