Structural description of dihedral extended Schottky groups and application in study of symmetries of handlebodies

Primer Autor
Gromadzki, Grzegorz
Co-autores
Hidalgo, Ruben A.
Título
Structural description of dihedral extended Schottky groups and application in study of symmetries of handlebodies
Editorial
ELSEVIER
Revista
TOPOLOGY AND ITS APPLICATIONS
Lenguaje
en
Resumen
Given a symmetry tau of a closed Riemann surface S, there exists an extended Kleinian group K, whose orientation-preserving half is a Schottky group Gamma uniformizing S, such that K/Gamma induces (tau), the group K is called an extended Schottky group. A geometrical structural description, in terms of the Klein-Maskit combination theorems, of both Schottky and extended Schottky groups is well known. A dihedral extended Schottky group is a group generated by the elements of two different extended Schottky groups, both with the same orientation-preserving half. Such configuration of groups corresponds to closed Riemann surfaces together with two different symmetries and the aim of this paper is to provide a geometrical structure of them. This result can be used in study of three dimensional manifolds and as an illustration we give the sharp upper bounds for the total number of connected components of the locus of fixed points of two and three different symmetries of a handlebody with a Schottky structure.(c) 2023 Elsevier B.V. All rights reserved.
Fecha Publicación
2023
Tipo de Recurso
artículo original
doi
10.1016/j.topol.2023.108568
Formato Recurso
PDF
Palabras Claves
Riemann surfaces
Schottky groups
Symmetries
Ubicación del archivo
http://dx.doi.org/10.1016/j.topol.2023.108568
Categoría OCDE
Matemáticas
Materias
superficies de Riemann
grupos Schottky
Simetrías
Identificador del recurso (Mandatado-único)
artículo original
Versión del recurso (Recomendado-único)
versión publicada
Derechos de acceso
metadata
Identificador relacionado
https://arxiv.org/pdf/1710.07518.pdf
Access Rights
metadata
Id de Web of Science
WOS:001083132500001
ISSN
0166-8641
Tipo de ruta
verde / hibrida
Categoría WOS
Matemáticas
Referencia del Financiador (Mandatado si es aplicable-repetible)
ANID-FONDECYT 1230001
ANID-FONDECYT 1220261
ANID-FONDECYT 1190001
NCN 2015/17/B/ST1/03235
ANID FONDECYT 1230001
ANID FONDECYT 1220261
ANID FONDECYT 1190001
Polish NCN 2015/17/B/ST1/03235
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