TY  - BOOK
AU  - Chiswell,Ian
AU  - Müller,T.W.
TI  - A universal construction for groups acting freely on real trees
T2  - Cambridge tracts in mathematics
SN  - 9781139176064 (ebook)
AV  - QA183 .C49 2012
U1  - 512.2 23
PY  - 2012///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Geometric group theory
KW  - Trees (Graph theory)
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); 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
N2  - 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
UR  - https://doi.org/10.1017/CBO9781139176064
ER  -