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Metric and analytic properties of R-trees

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
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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Contributors

Author: Claire Louise Vatcher

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