Dessins d'enfants on Riemann surfaces [electronic resource] / Gareth A. Jones, Jürgen Wolfart.
2016
QA613.2
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Title
Dessins d'enfants on Riemann surfaces [electronic resource] / Gareth A. Jones, Jürgen Wolfart.
ISBN
9783319247113 (electronic book)
3319247115 (electronic book)
9783319247090
3319247115 (electronic book)
9783319247090
Published
Cham : Springer, [2016]
Copyright
©2016
Language
English
Description
1 online resource.
Item Number
10.1007/978-3-319-24711-3 doi
Call Number
QA613.2
Dewey Decimal Classification
514/.3
Summary
This volume provides an introduction to dessins d'enfants and embeddings of bipartite graphs in compact Riemann surfaces. The first part of the book presents basic material, guiding the reader through the current field of research. A key point of the second part is the interplay between the automorphism groups of dessins and their Riemann surfaces, and the action of the absolute Galois group on dessins and their algebraic curves. It concludes by showing the links between the theory of dessins and other areas of arithmetic and geometry, such as the abc conjecture, complex multiplication and Beauville surfaces. Dessins d'Enfants on Riemann Surfaces will appeal to graduate students and all mathematicians interested in maps, hypermaps, Riemann surfaces, geometric group actions, and arithmetic.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Added Author
Wolfart, Jürgen, author.
Series
Springer monographs in mathematics.
Available in Other Form
Print version: 9783319247090
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Table of Contents
Historical and introductory background
Graph embeddings
Dessins and triangle groups
Galois actions
Quasiplatonic surfaces, and automorphisms
Regular maps
Regular embeddings of complete graphs
Wilson operations
Further examples
Arithmetic aspects
Beauville surfaces.
Graph embeddings
Dessins and triangle groups
Galois actions
Quasiplatonic surfaces, and automorphisms
Regular maps
Regular embeddings of complete graphs
Wilson operations
Further examples
Arithmetic aspects
Beauville surfaces.