TY  - BOOK
AU  - Jones,Gareth A.
AU  - Wolfart,Jürgen
ED  - SpringerLink (Online service)
TI  - Dessins d'Enfants on Riemann Surfaces
T2  - Springer Monographs in Mathematics,
SN  - 9783319247113
AV  - QA564-609 
U1  - 516.35 23
PY  - 2016///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Mathematics
KW  - Algebraic geometry
KW  - Group theory
KW  - Functions of complex variables
KW  - Hyperbolic geometry
KW  - Algebraic Geometry
KW  - Group Theory and Generalizations
KW  - Functions of a Complex Variable
KW  - Several Complex Variables and Analytic Spaces
KW  - Hyperbolic Geometry
KW  - Electronic books
KW  - local
N1  - 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
N2  - 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
UR  - http://ezproxy.alfaisal.edu/login?url=http://dx.doi.org/10.1007/978-3-319-24711-3
ER  -