Overview
- Provides basic material about maps and hypermaps on Riemann surfaces
- Presents many elementary and less elementary examples of Galois actions on dessins and their algebraic curves
- Emphasises the role of group theory in the classification of regular maps, regular dessins, and quasiplatonic surfaces
- Explains the links between the theory of dessins and other areas of arithmetic and geometry
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (11 chapters)
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Front Matter
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Basic Material
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Front Matter
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Regular Dessins
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Front Matter
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Applications
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“The book under review provides a very useful insight into the theory of dessins, and on its deep relationship with a number of mathematical distant fields. It is excellently written, and the Chapters are somewhat independent, in the sense that they have their own abstract, keywords and references. Of course, it is worth noting that the authors have contributed themselves to many of the results included in the book, most of which are really recent.” (José Javier Etayo, zbMATH, August, 2017)
“This book allows the reader familiar with the analytic aspects of the theory of Riemann surfaces to develop a feeling for the arithmetic aspects of these objects. … The reader interested in diving deeper into any of these aspects will most certainly find this well-written book to be of much help.” (Ariyan Javanpeykar, Mathematical Reviews, January, 2017)
“The book is intended for properly trained mathematics graduate students or researchers. … The text is also regularly interrupted by formulations of exercises which ask to prove some intermediate result or apply a definition in a particular situation (some brief hints are added at the end of the book). The book can thus be used as a textbook for a course on this fascinating topic.” (Adhemar Bultheel, European Mathematical Society, euro-math-soc.eu, April, 2016)
Authors and Affiliations
Bibliographic Information
Book Title: Dessins d'Enfants on Riemann Surfaces
Authors: Gareth A. Jones, Jürgen Wolfart
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-24711-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-24709-0Published: 05 April 2016
Softcover ISBN: 978-3-319-79664-2Published: 19 April 2018
eBook ISBN: 978-3-319-24711-3Published: 23 March 2016
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XIV, 259
Number of Illustrations: 41 illustrations in colour
Topics: Algebraic Geometry, Group Theory and Generalizations, Functions of a Complex Variable, Several Complex Variables and Analytic Spaces, Hyperbolic Geometry