Metric and analytic properties of R-trees
Metric and analytic properties of R-trees
In this thesis we consider metric and analytic properties of non-discrete metric spaces. The particular example we work with is that of ℝ-trees. We construct large scale Lipschitz maps which we use to prove that the Hilbert space compression of ℝ-trees is equal to one. We provide an overview of the current variations of property A and move on to develop some new definitions. We then discuss which classes of ℝ-trees have property A, also know as a weak form of amenability. Finally we review linking property A, uniform embeddability and exactness.
University of Southampton
Vatcher, Claire Louise
6e0f6ee7-247f-4019-a96d-df800fbed4b9
2006
Vatcher, Claire Louise
6e0f6ee7-247f-4019-a96d-df800fbed4b9
Vatcher, Claire Louise
(2006)
Metric and analytic properties of R-trees.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
In this thesis we consider metric and analytic properties of non-discrete metric spaces. The particular example we work with is that of ℝ-trees. We construct large scale Lipschitz maps which we use to prove that the Hilbert space compression of ℝ-trees is equal to one. We provide an overview of the current variations of property A and move on to develop some new definitions. We then discuss which classes of ℝ-trees have property A, also know as a weak form of amenability. Finally we review linking property A, uniform embeddability and exactness.
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Published date: 2006
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Local EPrints ID: 465948
URI: http://eprints.soton.ac.uk/id/eprint/465948
PURE UUID: eadee0bb-55ae-4a5d-988e-d2783e2df573
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Date deposited: 05 Jul 2022 03:45
Last modified: 16 Mar 2024 20:27
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Author:
Claire Louise Vatcher
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