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The Grothendieck Theory of Dessins d'Enfants : London Mathematical Society Lecture Notes - Leila Schneps

The Grothendieck Theory of Dessins d'Enfants

London Mathematical Society Lecture Notes

Paperback

Published: 26th September 1994
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The focus of this book is on combinatorial objects, dessins d'enfants, which are drawings with vertices and edges on topological surfaces. Their interest lies in their relation with the set of algebraic curves defined over the closure of the rationals, and the corresponding action of the absolute Galois group on them. The articles contained here unite basic elements of the subject with recent advances. Topics covered include: the explicity association of algebraic curves to dessins, the study of the action of the Galois group on the dessins, computation and combinatorics, relations with modular forms, geometry, generating functions, TeichmUller and moduli spaces. Researchers in number theory, algebraic geometry or related areas of group theory will find much of interest in this book.

Noncongruence subgroups, covers, and drawings
Dessins d'enfant on the Riemann sphere
Dessins from a geometric point of view
Maps, hypermaps and triangle groups
Fields of definition of some three point ramified field extensions
On the classification of plane trees by their Galois orbit
Triangulations
Dessins d'enfant and Shimura varieties
Horizontal divisors on arithmetic surfaces associated with Belyi uniformizations
Algebraic representation of the Teichm1/4ller spaces
On the embedding of Gal(Q/Q) into GT
Appendix
The Grothendieck-Teichm1/4ller group and automorphisms of braid groups
Moore and Seiberg equations, topological field theories and Galois theory
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521478212
ISBN-10: 0521478219
Series: London Mathematical Society Lecture Notes
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 380
Published: 26th September 1994
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 23.01 x 15.49  x 2.41
Weight (kg): 0.62