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OverviewThe 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. Full Product DetailsAuthor: Ian Chiswell (Queen Mary University of London) , Thomas Müller (Queen Mary University of London)Publisher: Cambridge University Press Imprint: Cambridge University Press (Virtual Publishing) Volume: 195 ISBN: 9781139176064ISBN 10: 1139176064 Publication Date: 05 November 2012 Audience: Professional and scholarly , Professional & Vocational Format: Undefined Publisher's Status: Active Availability: In stock  We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of ContentsPreface; 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.ReviewsAuthor InformationIan 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 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. Tab Content 6Author Website:Countries AvailableAll regions |
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