Author	Jones, Gareth A. author
Title	Dessins d'Enfants on Riemann Surfaces [electronic resource] / by Gareth A. Jones, Jürgen Wolfart
Imprint	Cham : Springer International Publishing : Imprint: Springer, 2016
Edition	1st ed. 2016
Connect to	http://dx.doi.org/10.1007/978-3-319-24711-3
Descript	XIV, 259 p. 41 illus. in color. online resource

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 -- 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

1. Mathematics
2. Algebraic geometry
3. Group theory
4. Functions of complex variables
5. Hyperbolic geometry
6. Mathematics
7. Algebraic Geometry
8. Group Theory and Generalizations
9. Functions of a Complex Variable
10. Several Complex Variables and Analytic Spaces
11. Hyperbolic Geometry