Geometric Galois Actions

doi:10.1017/CBO9780511666124

This book surveys progress in the domains described in the hitherto unpublished manuscript 'Esquisse d'un Programme' (Sketch of a Program) by Alexander Grothendieck. It will be of wide interest amongst workers in algebraic geometry, number theory, algebra and topology.

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Geometric Galois Actions

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Introduction
pp vii-x

Abstracts
pp 1-10

Part I - Dessins d'enfants
pp 11-12

Unicellular cartography and Galois orbits of plane trees
pp 13-24

Galois groups, monodromy groups and cartographic groups
pp 25-66

Permutation techniques for coset representations of modular subgroups
pp 67-78

Dessins d'enfants en genre 1
pp 79-116

Part II - Inverse Galois problem
pp 117-118

The regular inverse Galois problem over large fields
pp 119-138

The symplectic braid group and Galois realizations
pp 139-150

Applying modular towers to the inverse Galois problem
pp 151-176

Part III - Galois actions, braids and mapping class groups
pp 177-178

Galois group Gℚ, singularity E7, and moduli M3
pp 179-218

Monodromy of iterated integrals and non–abelian unipotent periods
pp 219-290

Part IV - Universal Teichmüller theory
pp 291-292

The universal Ptolemy group and its completions
pp 293-312

Sur l'isomorphisme du groupe de Richard Thompson avec le groupe de Ptolémée
pp 313-324

The universal Ptolemy-Teichmuller groupoid
pp 325-348

Errata for Tame and stratified objects
pp 349-349

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