The engaging symmetry of Riemann surfaces: A historical perspective
The engaging symmetry of Riemann surfaces: A historical perspective
The historical development of Riemann surfaces, starting in the late 1800’s, was driven in large part by the study of highly symmetrical surfaces. Not only do these surfaces have an engaging beauty, but they have very strong interconnections with other structures such as maps on a surface. In this expository article we first develop the basics of Riemann surfaces and their automorphism groups, laying out the tools for the historical treatment of the highly symmetrical surfaces in the later sections. The main topics of the later sections will be Hurwitz surfaces and groups, maps and dessins d’enfant on surfaces, and platonic and quasiplatonic surfaces and groups. For the novice reader, the introductory material will also be helpful background for reading some of the other papers in this volume, particularly the companion article on future directions in the field.
Automorphisms, Dessin d’enfant, Riemann surface, Triangle group
1-35
Broughton, S. Allen
e035076b-5701-4800-8267-1419441f4321
Jones, Gareth A.
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Singerman, David
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31 December 2022
Broughton, S. Allen
e035076b-5701-4800-8267-1419441f4321
Jones, Gareth A.
fdb7f584-21c5-4fe4-9e57-b58c78ebe3f5
Singerman, David
3eeb0783-c87c-4405-81d7-e80ae4c15f8b
Broughton, S. Allen, Jones, Gareth A. and Singerman, David
(2022)
The engaging symmetry of Riemann surfaces: A historical perspective.
In,
Wootton, Aaron, Broughton, S. Allen and Paulhus, Jennifer
(eds.)
Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics.
(Contemporary mathematics, 776)
.
(doi:10.1090/wootton/776).
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Book Section
Abstract
The historical development of Riemann surfaces, starting in the late 1800’s, was driven in large part by the study of highly symmetrical surfaces. Not only do these surfaces have an engaging beauty, but they have very strong interconnections with other structures such as maps on a surface. In this expository article we first develop the basics of Riemann surfaces and their automorphism groups, laying out the tools for the historical treatment of the highly symmetrical surfaces in the later sections. The main topics of the later sections will be Hurwitz surfaces and groups, maps and dessins d’enfant on surfaces, and platonic and quasiplatonic surfaces and groups. For the novice reader, the introductory material will also be helpful background for reading some of the other papers in this volume, particularly the companion article on future directions in the field.
Text
history of Riemann surface symmetry
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Accepted/In Press date: 18 September 2019
Published date: 31 December 2022
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Keywords:
Automorphisms, Dessin d’enfant, Riemann surface, Triangle group
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Local EPrints ID: 468825
URI: http://eprints.soton.ac.uk/id/eprint/468825
PURE UUID: a445d7cc-7729-4e2b-8968-fed7b920b963
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Date deposited: 26 Aug 2022 16:44
Last modified: 05 Jun 2024 19:58
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Contributors
Author:
S. Allen Broughton
Author:
Gareth A. Jones
Editor:
Aaron Wootton
Editor:
S. Allen Broughton
Editor:
Jennifer Paulhus
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