A Universal Construction for Groups Acting Freely on Real Trees(English, Hardcover, Chiswell Ian)

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A Universal Construction for Groups Acting Freely on Real Trees(English, Hardcover, Chiswell Ian) is written by Chiswell Ian and published by Cambridge University Press. It's available with International Standard Book Number or ISBN identification 1107024811 (ISBN 10) and 9781107024816 (ISBN 13).

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.