### Impacto

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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Official URL: http://www.sciencedirect.com/science/article/pii/S0166864110001987

## Abstract

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 |
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Uncontrolled Keywords: | Group actions in low dimensions; Fuchsian groups and their generalizations |

Subjects: | Sciences > Mathematics > Geometry |

ID Code: | 15716 |

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Deposited On: | 21 Jun 2012 10:52 |

Last Modified: | 06 Feb 2014 10:30 |

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