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Dessins d'enfants on Riemann surfaces

Jones, Gareth A.

Dessins d'enfants on Riemann surfaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	Dessins d'enfants on Riemann surfacesby Gareth A. Jones, Jurgen Wolfart.
Author:	Jones, Gareth A.
other author:	Wolfart, Jurgen.
Published:	Cham :Springer International Publishing :2016.
Description:	xiv, 259 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Dessins d'enfants (Mathematics)
Online resource:	http://dx.doi.org/10.1007/978-3-319-24711-3
ISBN:	9783319247113$q(electronic bk.)

Dessins d'enfants on Riemann surfaces
Jones, Gareth A.

Dessins d'enfants on Riemann surfaces[electronic resource] /by Gareth A. Jones, Jurgen Wolfart. - Cham :Springer International Publishing :2016. - xiv, 259 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

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.

ISBN: 9783319247113$q(electronic bk.)

Standard No.: 10.1007/978-3-319-24711-3doiSubjects--Topical Terms:

742183
Dessins d'enfants (Mathematics)

LC Class. No.: QA613.2

Dewey Class. No.: 514.3

Dessins d'enfants on Riemann surfaces
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490 1 $a Springer monographs in mathematics, $x 1439-7382
505 0 $a 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.
520 $a 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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650 2 4 $a Group Theory and Generalizations. $3 274819
650 2 4 $a Functions of a Complex Variable. $3 275780
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650 2 4 $a Hyperbolic Geometry. $3 684054
700 1 $a Wolfart, Jurgen. $3 742182
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