Format:
1 Online-Ressource (xiii, 285 pages)
,
digital, PDF file(s).
ISBN:
9781139176064
Series Statement:
Cambridge tracts in mathematics 195
Content:
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.
Content:
1. Introduction -- 2. The group R F (G) -- 3. The R-tree X[g subscript] associated with RF (G) -- 4. Free R-tree actions and universality -- 5. Exponent sums -- 6. Functionality -- 7. Conjugacy of hyperbolic elements -- 8. The centalisers of hyperbolic elements -- 9. Test functions: basic theory and first applications -- 10. Test functions: existence theorem and further applications -- 11. A generation to groupoids -- Appendices
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9781107024816
Additional Edition:
ISBN 9781107024816
Additional Edition:
Erscheint auch als Chiswell, Ian, 1948 - A universal construction for groups acting freely on real trees Cambridge [u.a.] : Cambridge Univ. Press, 2012 ISBN 1107024811
Additional Edition:
ISBN 9781107024816
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9781107024816
Language:
English
Subjects:
Mathematics
DOI:
10.1017/CBO9781139176064
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