Repositorio
Institucional

Gromadzki, Grzegorz

Hidalgo, Ruben A.

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

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TOPOLOGY AND ITS APPLICATIONS

en

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.

2023

artículo original

10.1016/j.topol.2023.108568

PDF

Riemann surfaces

Schottky groups

Symmetries

Matemáticas

superficies de Riemann

grupos Schottky

Simetrías

artículo original

versión publicada

metadata

https://arxiv.org/pdf/1710.07518.pdf

metadata

WOS:001083132500001

0166-8641

verde / hibrida

Matemáticas

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