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A universal construction for groups ...

Chiswell, Ian, (1948-)

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A universal construction for groups acting freely on real trees

Record Type:	Electronic resources : Monograph/item
Title/Author:	A universal construction for groups acting freely on real trees/ Ian Chiswell and Thomas Muller.
Author:	Chiswell, Ian,
other author:	Muller, T. W.
Published:	Cambridge :Cambridge University Press, : 2012.,
Description:	xiii, 285 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
[NT 15003449]:	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.
Subject:	Geometric group theory. -
Online resource:	https://doi.org/10.1017/CBO9781139176064
ISBN:	9781139176064

A universal construction for groups acting freely on real trees
Chiswell, Ian,1948-

A universal construction for groups acting freely on real trees[electronic resource] /Ian Chiswell and Thomas Muller. - Cambridge :Cambridge University Press,2012. - xiii, 285 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;195. - Cambridge tracts in mathematics ;195..

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.

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.

ISBN: 9781139176064Subjects--Topical Terms:

745240
Geometric group theory.

LC Class. No.: QA183 / .C49 2012

Dewey Class. No.: 512.2

A universal construction for groups acting freely on real trees
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100 1 $a Chiswell, Ian, $d 1948- $3 1050684
245 1 2 $a A universal construction for groups acting freely on real trees $h [electronic resource] / $c Ian Chiswell and Thomas Muller.
260 $a Cambridge : $b Cambridge University Press, $c 2012.
300 $a xiii, 285 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge tracts in mathematics ; $v 195
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a 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.
520 $a 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.
650 0 $a Geometric group theory. $3 745240
650 0 $a Trees (Graph theory) $3 648365
700 1 $a Muller, T. W. $q (Thomas Wolfgang), $d 1957- $3 3470476
830 0 $a Cambridge tracts in mathematics ; $v 195. $3 3470477
856 4 0 $u https://doi.org/10.1017/CBO9781139176064