Dessins d'Enfants on Riemann Surfaces

AvGareth A. Jones,Jürgen Wolfart

Inbunden, Engelska, 2016

Del i serien Springer Monographs in Mathematics

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2016-04-05
Mått:155 x 235 x 21 mm
Vikt:582 g
Format:Inbunden
Språk:Engelska
Serie:Springer Monographs in Mathematics
Antal sidor:259
Upplaga:16001
Förlag:Springer International Publishing AG
ISBN:9783319247090

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

"This book allows the reader familiar with the analytic aspects of the theory of Riemann surfaces to develop a feeling for the arithmetic aspects of these objects. ... The reader interested in diving deeper into any of these aspects will most certainly find this well-written book to be of much help." (Ariyan Javanpeykar, Mathematical Reviews, January, 2017) "The book is intended for properly trained mathematics graduate students or researchers. ... The text is also regularly interrupted by formulations of exercises which ask to prove some intermediate result or apply a definition in a particular situation (some brief hints are added at the end of the book). The book can thus be used as a textbook for a course on this fascinating topic." (Adhemar Bultheel, European Mathematical Society, euro-math-soc.eu, April, 2016)

Innehållsförteckning

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.