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  3. A Universal Construction for Groups Acting Freely on Real Trees
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  • Publisher:
    Cambridge University Press
    Publication date:
    05 November 2012
    18 October 2012
    ISBN:
    9781139176064
    9781107024816
    DOI:
    https://doi.org/10.1017/CBO9781139176064
    Dimensions:
    (228 x 152 mm)
    Weight & Pages:
    0.56kg, 297 Pages
    Dimensions:
    Weight & Pages:
    • Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    Cambridge Tracts in Mathematics (195)
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    Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    Cambridge Tracts in Mathematics (195)
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    Book description

    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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