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Birkhäuser

Sur les Groupes Hyperboliques d’après Mikhael Gromov

  • Book
  • © 1990

Overview

Editors:
  1. Etienne Ghys

    1. Laboratoire de Mathématiques, Ecole Normale Supérieure de Lyon, Lyon Cedex 07, France

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  2. Pierre Harpe

    1. Section de Mathématiques, Université de Genève, Geneva 24, Switzerland

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Progress in Mathematics (PM, volume 83)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xi
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  2. Panorama

    • Etienne Ghys, Pierre de la Harpe
    Pages 1-25

  3. Espaces Métriques Hyperboliques

    • Etienne Ghys, Pierre de la Harpe
    Pages 27-45

  4. Espaces à Courbure Négative et Groupes Hyperboliques

    • Marc Troyanov
    Pages 47-66

  5. Premières Propriétés des Groupes Hyperboliques

    • Eliane Salem
    Pages 67-77

  6. Quasi-Isométries et Quasi-Géodésiques

    • Etienne Ghys, Pierre de la Harpe
    Pages 79-102

  7. Le Bord D’un Arbre

    • Etienne Ghys, Pierre de la Harpe
    Pages 103-116

  8. Le Bord D’un Espace Hyperbolique

    • Etienne Ghys, Pierre de la Harpe
    Pages 117-134

  9. L’action au Bord des Isométries

    • Etienne Ghys, Pierre de la Harpe
    Pages 135-163

  10. La Propriété de Markov Pour les Groupes Hyperboliques

    • Etienne Ghys, Pierre de la Harpe
    Pages 165-187

  11. Singular Spaces of Non-Positive Curvature

    • Werner Ballmann
    Pages 189-201

  12. Orbi-Espaces

    • André Haefliger
    Pages 203-213

  13. Groupes de Torsion

    • Etienne Ghys, André Haefliger
    Pages 215-226

  14. Back Matter

    Pages 227-286
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Keywords

About this book

The theory of hyperbolic groups has its starting point in a fundamental paper by M. Gromov, published in 1987. These are finitely generated groups that share important properties with negatively curved Riemannian manifolds. 

This monograph is intended to be an introduction to part of Gromov's theory, giving basic definitions, some of the most important examples, various properties of hyperbolic groups, and an application to the construction of infinite torsion groups. The main theme is the relevance of geometric ideas to the understanding of finitely generated groups. In addition to chapters written by the editors, contributions by W. Ballmann, A. Haefliger, E. Salem, R. Strebel, and M. Troyanov are also included.


The book will be particularly useful to researchers in combinatorial group theory, Riemannian geometry, and theoretical physics, as well as post-graduate students interested in these fields. 

Editors and Affiliations

  • Laboratoire de Mathématiques, Ecole Normale Supérieure de Lyon, Lyon Cedex 07, France

    Etienne Ghys

  • Section de Mathématiques, Université de Genève, Geneva 24, Switzerland

    Pierre Harpe

Bibliographic Information

  • Book Title: Sur les Groupes Hyperboliques d’après Mikhael Gromov

  • Editors: Etienne Ghys, Pierre Harpe

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4684-9167-8

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1990

  • Softcover ISBN: 978-0-8176-3508-4Published: 01 January 1990

  • eBook ISBN: 978-1-4684-9167-8Published: 11 December 2013

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: XI, 287

  • Topics: Group Theory and Generalizations, Algebraic Geometry, Algebra

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