Geometric Galois Actions, Volume 2: The Inverse Galois Problem, Moduli Spaces, and Mapping Class Groups

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This book surveys progress in the domains described in the hitherto unpublished manuscript "Esquisse d'un Programme" (Sketch of a Program) by Alexander Grothendieck.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.

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Table of Contents

List of participants; Abstracts of the talks; Part I. Introduction: Part II. Abstracts: Part III. Dessins d'enfants: 1. Unicellular cartography and Galois orbits of plane trees N. Adrianov, G. Shabat; 2. Galois groups, monodromy groups and cartographical groups G. Jones, M. Streit; 3. Drawings, triangle groups and algebraic curves W. Harvey; 4. Permutation techniques for coset representations of modular subgroups T. Hsu; 5. On groups acting on dessin-labeled objects V. Shabat; 6. Dessins d'enfants en genre 1 L. Zapponi; Part IV. Inverse Galois Problem: 7. The regular inverse Galois problem over large fields P. Debes, B. Deschamps; 8. The symplectic braid group and Galois realizations K. Strambach, H. Volklein; 9. Obstructed components of A5 modular towers M. Fried, Y. Kopeliovic; Part V. Galois Actions And Mapping Class Groups: 10. Monodromy of iterated integrals (non-Abelian unipotent periods) Z. Wojtkowiak; 11. Deformation of singularities and mapping class groups M. Matsumoto; Part VI. Universal Teichmüller Theory: 12. The universal Ptolemy group and its completions R. Penner; 13. Sur l'isomorphisme du groupe de Richard Thompson avec le groupe de Ptolémée M. Imbert, V. Sergiescu; 14. The universal Ptolemy–Teichmuller groupoid P. Lochak, L. Schneps.

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