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Dessins d'Enfants on Riemann Surfaces

  • Gareth A. Jones
  • Jürgen Wolfart

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Basic Material

    1. Front Matter
      Pages 1-1
    2. Gareth A. Jones, Jürgen Wolfart
      Pages 3-39
    3. Gareth A. Jones, Jürgen Wolfart
      Pages 41-58
    4. Gareth A. Jones, Jürgen Wolfart
      Pages 59-87
    5. Gareth A. Jones, Jürgen Wolfart
      Pages 89-111
  3. Regular Dessins

    1. Front Matter
      Pages 113-113
    2. Gareth A. Jones, Jürgen Wolfart
      Pages 115-151
    3. Gareth A. Jones, Jürgen Wolfart
      Pages 153-161
    4. Gareth A. Jones, Jürgen Wolfart
      Pages 163-177
    5. Gareth A. Jones, Jürgen Wolfart
      Pages 179-192
    6. Gareth A. Jones, Jürgen Wolfart
      Pages 193-210
  4. Applications

    1. Front Matter
      Pages 211-211
    2. Gareth A. Jones, Jürgen Wolfart
      Pages 213-224
    3. Gareth A. Jones, Jürgen Wolfart
      Pages 225-249
  5. Back Matter
    Pages 251-259

About this book

Introduction

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.

Keywords

Dessins d'enfants Riemann surfaces Algebraic curves Belyi functions Triangle groups Cartographic groups Quasiplatonic surfaces ABC problem

Authors and affiliations

  • Gareth A. Jones
    • 1
  • Jürgen Wolfart
    • 2
  1. 1.School of MathematicsUniversity of SouthamptonSouthamptonUnited Kingdom
  2. 2.Johann Wolfgang Goethe-UniversitätFrankfurt am MainGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-24711-3
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-24709-0
  • Online ISBN 978-3-319-24711-3
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site