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A Universal Construction for Groups Acting Freely on Real Trees

A Universal Construction for Groups Acting Freely on Real Trees

Part of Cambridge Tracts in Mathematics

  • Date Published: October 2012
  • availability: In stock
  • format: Hardback
  • isbn: 9781107024816


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About the Authors
  • The theory of R-trees is a well-established and important area of geometric group theory and in this book the authors introduce a construction that provides a new perspective on group actions on R-trees. They construct a group RF(G), equipped with an action on an R-tree, whose elements are certain functions from a compact real interval to the group G. They also study the structure of RF(G), including a detailed description of centralizers of elements and an investigation of its subgroups and quotients. Any group acting freely on an R-tree embeds in RF(G) for some choice of G. Much remains to be done to understand RF(G), and the extensive list of open problems included in an appendix could potentially lead to new methods for investigating group actions on R-trees, particularly free actions. This book will interest all geometric group theorists and model theorists whose research involves R-trees.

    • A coherent introduction to an exciting new area of research
    • Contains many open problems to encourage further study
    • The basic theory of Λ-trees is presented in an appendix
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    Product details

    • Date Published: October 2012
    • format: Hardback
    • isbn: 9781107024816
    • length: 297 pages
    • dimensions: 235 x 158 x 20 mm
    • weight: 0.56kg
    • contains: 4 b/w illus. 65 exercises
    • availability: In stock
  • Table of Contents

    1. Introduction
    2. The group RF(G)
    3. The R-tree XG associated with RF(G)
    4. Free R-tree actions and universality
    5. Exponent sums
    6. Functoriality
    7. Conjugacy of hyperbolic elements
    8. The centralizers of hyperbolic elements
    9. Test functions: basic theory and first applications
    10. Test functions: existence theorem and further applications
    11. A generalization to groupoids
    Appendix A. The basics of Λ-trees
    Appendix B. Some open problems

  • Authors

    Ian Chiswell, Queen Mary University of London
    Ian Chiswell is Emeritus Professor in the School of Mathematical Sciences at Queen Mary, University of London. His main area of research is geometric group theory, especially the theory of Λ-trees. Other interests have included cohomology of groups and ordered groups.

    Thomas Müller, Queen Mary University of London
    Thomas Müller is Professor in the School of Mathematical Sciences at Queen Mary, University of London. His main research interests are in geometric, combinatorial and asymptotic group theory, in algebraic combinatorics, number theory and (mostly complex) analysis.

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