Geometric Galois Actions: Volume 2, The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups (London Mathematical Society Lecture Note Series, Series Number 243)

This book surveys progress in the domains described in the hitherto unpublished manuscript "Esquisse d'un Programme" (Sketch of a Program) by Alexander Grothendieck.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 among workers in algebraic geometry, number theory, algebra and topology. Cover......Page 1 Geometric Galois Actions Volume 2: The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups......Page 4 9780521596411......Page 5 Table of Contents......Page 6 Introduction......Page 8 Abstracts of the talks......Page 12 Part I. Dessins d'enfants......Page 22 Unicellular Cartography and Galois Orbits of Plane Trees......Page 24 Galois Groups, Monodromy Groups and Cartographic Groups......Page 36 Permutation techniques for coset representations of modular subgroups......Page 78 Dessins d'enfants en genre 1......Page 90 Part II. The Inverse Galois Problem......Page 128 The Regular Inverse Galois Problem over Large Fields......Page 130 The Symplectic Braid Group and Galois Realizations......Page 150 Applying Modular Towers to the Inverse Galois Problem......Page 162 Part III. Galois actions and mapping class groups......Page 188 Galois group G_{\mathbb{Q}}, Singularity E_7, and Moduli M_3......Page 190 Monodromy of Iterated Integrals and Non-abelian Unipotent Periods......Page 230 Part IV. Universal Teichmuller theory......Page 302 The Universal Ptolemy Group and Its Completions......Page 304 Sur l'isomorphisme du groupe de Richard Thompson avec le groupe de Ptolemee......Page 324 The universal Ptolemy-Teichmuller groupoid......Page 336 Errata for Tame and stratified objects (This article appeared in volume I of Geometric Galois Actions)......Page 360 This book surveys progress in the domains described in the hitherto unpublished manuscript 'Esquisse d'un Programme' (Sketch of a Program) by Alexander Grothendieck.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. 1. Around Grothendieck's Esquisse d'un programme 2. The inverse Galois problem, moduli spaces, and mapping class groups.