TY - BOOK ID - 7227653 TI - A universal construction for groups acting freely on real trees AU - Chiswell, Ian AU - Mùˆller, T. W. PY - 2012 VL - 195 SN - 9781107024816 1107024811 9781139176064 9781139569231 1139569236 1139176064 9781139571043 1139571044 9781139572798 1139889176 1139579614 1139573551 1139572792 PB - Cambridge : Cambridge University Press, DB - UniCat KW - Geometric group theory. KW - Trees (Graph theory) KW - Trees (Graph theory). KW - Database searching. KW - Computer algorithms. KW - Data structures (Computer science) KW - Information structures (Computer science) KW - Structures, Data (Computer science) KW - Structures, Information (Computer science) KW - Electronic data processing KW - File organization (Computer science) KW - Abstract data types (Computer science) KW - Algorithms KW - Data base searching KW - Database search strategies KW - Search strategies in databases KW - Searching databases KW - Electronic information resource searching KW - Graph theory KW - Group theory UR - https://www.unicat.be/uniCat?func=search&query=sysid:7227653 AB - 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. ER -