The Grothendieck Theory of Dessins d'Enfants

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Paperback | 26 September 1994

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380 Pages

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22.86 x 15.24 x 2.16

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Dessins d'Enfants are combinatorial objects, namely 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 study of this group via such realted combinatorial methods as its action on the Dessins and on certain fundamental groups of moduli spaces was initiated by Alexander Grothendieck in his unpublished Esquisse d'un Programme, and developed by many of the mathematicians who have contributed to this volume. The various articles here unite all of the basics of the subject as well as the most recent advances. Researchers in number theory, algebraic geometry or related areas of group theory will find much of interest in this book.

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You Can Find This Book In

Non-Fiction Mathematics Topology Combinatorics & Graph Theory Algebra Geometry Applied Mathematics

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.

The Grothendieck Theory of Dessins d'Enfants

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