© 2007

Geometric Group Theory

Geneva and Barcelona Conferences

  • Goulnara N. Arzhantseva
  • José Burillo
  • Laurent Bartholdi
  • Enric Ventura


  • Contains contributions from experts in geometric and combinatorial group theory, most of which were present at the Geneva and Barcelona conferences in 2005

  • Above the diversity of the articles included in this volume reigns a strong unity of themes and purposes: understanding geometrical and logical objects through their symmetries

  • Witnesses to the power of group theory as a language for expressing, communicating and solving problems throughout mathematics

  • Contains particularly two articles by A. Juhász on the solution of the membership problem for Magnus subgroups and on the solution of the conjugacy problem and malnormality of subgroups

Conference proceedings

Part of the Trends in Mathematics book series (TM)

Table of contents

  1. Front Matter
    Pages i-vii
  2. José Burillo, Sean Cleary, Bert Wiest
    Pages 21-35
  3. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 37-44
  4. Yves de Cornulier, Avinoam Mann
    Pages 45-50
  5. Ramón J. Flores
    Pages 51-64
  6. Vincent Guirardel, Gilbert Levitt
    Pages 65-73
  7. Yves de Cornulier, Pierre de la Harpe
    Pages 75-102
  8. Abderezak Ould Houcine
    Pages 103-119
  9. Alexei Miasnikov, Enric Ventura, Pascal Weil
    Pages 225-253

About these proceedings


This volume assembles research papers in geometric and combinatorial group theory. This wide area may be defined as the study of those groups that are defined by their action on a combinatorial or geometric object, in the spirit of Klein’s programme.

The contributions range over a wide spectrum: limit groups, groups associated with equations, with cellular automata, their structure as metric objects, their decomposition, etc. Their common denominator is the language of group theory, used to express and solve problems ranging from geometry to logic.


Geometric group theory Group theory classifying space conjugacy problem free group membership problem

Editors and affiliations

  • Goulnara N. Arzhantseva
    • 1
  • José Burillo
    • 2
  • Laurent Bartholdi
    • 3
  • Enric Ventura
    • 4
  1. 1.Section de mathématiquesUniversité de GenèveGenève 4Switzerland
  2. 2.Departament de Matemàtica Aplicada IVUniversitat Politècnica de Catalunya Escola Politècnica Superior de Castelldefels AvdaCastelldefels (Barcelona)Spain
  3. 3.Institut de Mathématiques B (IMB)École Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland
  4. 4.Department of Applied Mathematics III Escola Politècnica Superior d’Enginyeria de ManresaUniversitat Politècnica de CatalunyaManresa / BarcelonaSpain

Bibliographic information

  • Book Title Geometric Group Theory
  • Book Subtitle Geneva and Barcelona Conferences
  • Editors Goulnara N. Arzhantseva
    Laurent Bartholdi
    Jose Burillo
    Enric Ventura
  • Series Title Trends in Mathematics
  • DOI
  • Copyright Information Birkhäuser Verlag AG 2007
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-7643-8411-1
  • eBook ISBN 978-3-7643-8412-8
  • Edition Number 1
  • Number of Pages VII, 256
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Group Theory and Generalizations
  • Buy this book on publisher's site