Dessins d'enfants on Riemann surfaces / Gareth A. Jones, Jürgen Wolfart.
- Cham [Switzerland] ; New York : Springer International Publishing, 
- Springer monographs in mathematics.
Springer monographs in mathematics
xiv, 259 pages : illustrations ; 24 cm
- Dessins d'enfants (Mathematics)
- 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.
- Historical and introductory background
Dessins and triangle groups
Quasiplatonic surfaces, and automorphisms
Regular embeddings of complete graphs
- Includes bibliographical references and index.
- Wolfart, Jürgen, author.
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