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Look Inside 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

Authors:
Ian Chiswell, Queen Mary University of London
Thomas Müller, Queen Mary University of London

Date Published: November 2012
availability: Available
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: November 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: Available
Table of Contents
Preface
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
References
Index.
Look Inside
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.