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Birkhäuser

Infinite Groups: Geometric, Combinatorial and Dynamical Aspects

  • Book
  • © 2005

Overview

Editors:
  1. Laurent Bartholdi

    1. Institut de Mathématiques, EPFL, Lausanne, Switzerland

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    You can also search for this editor in PubMed   Google Scholar

  2. Tullio Ceccherini-Silberstein

    1. Dipartimento di Ingegneria, Università del Sannio, Benevento, Italy

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    You can also search for this editor in PubMed   Google Scholar

  3. Tatiana Smirnova-Nagnibeda

    1. Section de mathématiques, Université de Genève, Geneva 4, Switzerland

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  4. Andrzej Zuk

    1. Institut de Mathématiques, Université Paris 7, Paris, France

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  • Survey papers on major topics of combinatorial, geometric and asymptotic group theory
  • Interdiscpiplinary approach: the primary focus is on strong connections between group theory and other areas of mathematics, such as ergodic theory and dynamical systems, geometry and topology, probability theory, operator algebras
  • Representative selection of recent developments in a very active area of mathematical research
  • Includes supplementary material: sn.pub/extras

Part of the book series: Progress in Mathematics (PM, volume 248)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-viii
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  2. Parafree Groups

    • Gilbert Baumslag
    Pages 1-14

  3. The Finitary Andrews-Curtis Conjecture

    • Alexandre V. Borovik, Alexander Lubotzky, Alexei G. Myasnikov
    Pages 15-30

  4. Cuts in Kähler Groups

    • Thomas Delzant, Misha Gromov
    Pages 31-55

  5. Algebraic Mapping-Class Groups of Orientable Surfaces with Boundaries

    • Warren Dicks, Edward Formanek
    Pages 57-116

  6. Solved and Unsolved Problems Around One Group

    • Rostislav Grigorchuk
    Pages 117-218

  7. Cubature Formulas, Geometrical Designs, Reproducing Kernels, and Markov Operators

    • Pierre de la Harpe, Claude Pache
    Pages 219-267

  8. Survey on Classifying Spaces for Families of Subgroups

    • Wolfgang Lück
    Pages 269-322

  9. Are Unitarizable Groups Amenable?

    • Gilles Pisier
    Pages 323-362

  10. Probabilistic Group Theory and Fuchsian Groups

    • Aner Shalev
    Pages 363-388

  11. Just Non-(abelian by P-type) Groups

    • Said Sidki
    Pages 389-402

  12. Infinite Algebras and Pro-p Groups

    • Efim Zelmanov
    Pages 403-413
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Keywords

About this book

This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics addressed in the book include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics, such as dynamical systems, geometry, operator algebras, probability theory, and others. This interdisciplinary approach makes the book interesting to a large mathematical audience.

Contributors:

G. Baumslag
A.V. Borovik
T. Delzant
W. Dicks
E. Formanek
R. Grigorchuk
M. Gromov
P. de la Harpe
A. Lubotzky
W. Lück
A.G. Myasnikov
C. Pache
G. Pisier
A. Shalev
S. Sidki
E. Zelmanov

Editors and Affiliations

  • Institut de Mathématiques, EPFL, Lausanne, Switzerland

    Laurent Bartholdi

  • Dipartimento di Ingegneria, Università del Sannio, Benevento, Italy

    Tullio Ceccherini-Silberstein

  • Section de mathématiques, Université de Genève, Geneva 4, Switzerland

    Tatiana Smirnova-Nagnibeda

  • Institut de Mathématiques, Université Paris 7, Paris, France

    Andrzej Zuk

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