The Grothendieck Theory of Dessins d'Enfants

The Grothendieck Theory of Dessins d'Enfants

by Leila Schneps
     
 

ISBN-10: 0521478219

ISBN-13: 9780521478212

Pub. Date: 09/28/1994

Publisher: Cambridge University Press

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

Overview

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, Teichmüller and moduli spaces. Researchers in number theory, algebraic geometry or related areas of group theory will find much of interest in this book.

Product Details

ISBN-13:
9780521478212
Publisher:
Cambridge University Press
Publication date:
09/28/1994
Series:
London Mathematical Society Lecture Note Series, #200
Pages:
380
Product dimensions:
5.98(w) x 8.98(h) x 0.83(d)

Table of Contents

1. Noncongruence subgroups, covers, and drawings B. Birch; 2. Dessins d'enfant on the Riemann sphere L. Schneps; 3. Dessins from a geometric point of view J-M. Couveignes and L. Granboulan; 4. Maps, hypermaps and triangle groups G. Jones and D. Singerman; 5. Fields of definition of some three point ramified field extensions G. Malle; 6. On the classification of plane trees by their Galois orbit G. Shabat; 7. Triangulations M. Bauer and C. Itzykson; 8. Dessins d'enfant and Shimura varieties P. Cohen; 9. Horizontal divisors on arithmetic surfaces associated with Belyi uniformizations Y. Ihara; 10. Algebraic representation of the Teichmüller spaces K. Saito; 11. On the embedding of Gal(Q/Q) into GT Y. Ihara; Appendix M. Emsalem and P. Lochak; 12. The Grothendieck–Teichmüller group and automorphisms of braid groups P. Lochak and L. Schneps; 13. Moore and Seiberg equations, topological field theories and Galois theory P. Degiovanni.

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >