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＜E-Book＞
Dessins d'Enfants on Riemann Surfaces / by Gareth A. Jones, Jürgen Wolfart
(Springer Monographs in Mathematics. ISSN:21969922)

Edition	1st ed. 2016.
Publisher	Cham : Springer International Publishing : Imprint: Springer
Year	2016
Size	XIV, 259 p. 41 illus. in color : online resource
Authors	*Jones, Gareth A author Wolfart, Jürgen author SpringerLink (Online service)
Subjects	LCSH:Algebraic geometry LCSH:Group theory LCSH:Functions of complex variables LCSH:Geometry, Hyperbolic FREE:Algebraic Geometry FREE:Group Theory and Generalizations FREE:Functions of a Complex Variable FREE:Several Complex Variables and Analytic Spaces FREE:Hyperbolic Geometry
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-24711-3

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