Dessins d'Enfants on Riemann Surfaces

Nonfiction, Science & Nature, Mathematics, Geometry, Algebra
Cover of the book Dessins d'Enfants on Riemann Surfaces by Gareth A. Jones, Jürgen Wolfart, Springer International Publishing
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Author: Gareth A. Jones, Jürgen Wolfart ISBN: 9783319247113
Publisher: Springer International Publishing Publication: March 23, 2016
Imprint: Springer Language: English
Author: Gareth A. Jones, Jürgen Wolfart
ISBN: 9783319247113
Publisher: Springer International Publishing
Publication: March 23, 2016
Imprint: Springer
Language: English

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.

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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.

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