A Universal Construction for Groups Acting Freely on Real Trees
Book Details
Format
Hardback or Cased Book
Book Series
Cambridge Tracts in Mathematics
ISBN-10
1107024811
ISBN-13
9781107024816
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
US
Country of Publication
GB
Publication Date
Oct 18th, 2012
Print length
297 Pages
Weight
558 grams
Dimensions
23.40 x 15.90 x 2.00 cms
Product Classification:
Groups & group theoryGeometry
Ksh 20,700.00
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The theory of R-trees is a well-established and important area of geometric group theory. In this book, the authors introduce a construction that provides a new perspective on group actions on R-trees and could lead to new directions for research in this field. Open problems are included for further study.
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.
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