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Geometrie et theorie des groupes

Les groupes hyperboliques de Gromov

  • Book
  • © 1990

Overview

Authors:
  1. Michel Coornaert
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  2. Thomas Delzant
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  3. Athanase Papadopoulos
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1441)

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-X
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  2. Espaces métriques hyperboliques

    • Michel Coornaert, Thomas Delzant, Athanase Papadopoulos
    Pages 1-15

  3. Bord d'un espace hyperbolique

    • Michel Coornaert, Thomas Delzant, Athanase Papadopoulos
    Pages 16-23

  4. Quasi-géodésiques et quasi-isométries dans les espaces hyperboliques

    • Michel Coornaert, Thomas Delzant, Athanase Papadopoulos
    Pages 24-42

  5. Groupes hyperboliques

    • Michel Coornaert, Thomas Delzant, Athanase Papadopoulos
    Pages 43-56

  6. Le polyèdre Pd(X)

    • Michel Coornaert, Thomas Delzant, Athanase Papadopoulos
    Pages 57-64

  7. Inégalités isopérimétriques et espaces hyperboliques

    • Michel Coornaert, Thomas Delzant, Athanase Papadopoulos
    Pages 65-80

  8. Inégalités isopérimétriques : une application

    • Michel Coornaert, Thomas Delzant, Athanase Papadopoulos
    Pages 81-89

  9. Approximation par des arbres

    • Michel Coornaert, Thomas Delzant, Athanase Papadopoulos
    Pages 90-96

  10. Classification des isométries

    • Michel Coornaert, Thomas Delzant, Athanase Papadopoulos
    Pages 97-105

  11. Parties quasi-convexes d'un espace hyperbolique

    • Michel Coornaert, Thomas Delzant, Athanase Papadopoulos
    Pages 106-123

  12. Structure métrique sur le bord d'un espace hyperbolique

    • Michel Coornaert, Thomas Delzant, Athanase Papadopoulos
    Pages 124-139

  13. Automates et groupes hyperboliques

    • Michel Coornaert, Thomas Delzant, Athanase Papadopoulos
    Pages 140-158

  14. Back Matter

    Pages 159-165
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Keywords

About this book

The book is an introduction of Gromov's theory of hyperbolic spaces and hyperbolic groups. It contains complete proofs of some basic theorems which are due to Gromov, and emphasizes some important developments on isoperimetric inequalities, automatic groups, and the metric structure on the boundary of a hyperbolic space.

Bibliographic Information

  • Book Title: Geometrie et theorie des groupes

  • Book Subtitle: Les groupes hyperboliques de Gromov

  • Authors: Michel Coornaert, Thomas Delzant, Athanase Papadopoulos

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0084913

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1990

  • Softcover ISBN: 978-3-540-52977-4Published: 12 September 1990

  • eBook ISBN: 978-3-540-46294-1Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 165

  • Topics: Group Theory and Generalizations, Algebraic Geometry

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