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  • © 1990

Sur les Groupes Hyperboliques d’après Mikhael Gromov

Birkhäuser

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
  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. Quasi-Isométries et Quasi-Géodésiques

    • Etienne Ghys, Pierre de la Harpe
    Pages 79-102
  5. Le Bord D’un Arbre

    • Etienne Ghys, Pierre de la Harpe
    Pages 103-116
  6. Le Bord D’un Espace Hyperbolique

    • Etienne Ghys, Pierre de la Harpe
    Pages 117-134
  7. L’action au Bord des Isométries

    • Etienne Ghys, Pierre de la Harpe
    Pages 135-163
  8. La Propriété de Markov Pour les Groupes Hyperboliques

    • Etienne Ghys, Pierre de la Harpe
    Pages 165-187
  9. Singular Spaces of Non-Positive Curvature

    • Werner Ballmann
    Pages 189-201
  10. Orbi-Espaces

    • André Haefliger
    Pages 203-213
  11. Groupes de Torsion

    • Etienne Ghys, André Haefliger
    Pages 215-226
  12. Back Matter

    Pages 227-286

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

Buy it now

Buying options

eBook USD 89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access