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Extending partial isomorphisms

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Title: Extending partial isomorphisms
Author(s): Slutskyy, Kostyantyn
Director of Research: Rosendal, Christian
Doctoral Committee Chair(s): van den Dries, Lou
Doctoral Committee Member(s): Solecki, Slawomir; Rosendal, Christian; Kapovich, Ilya
Department / Program: Mathematics
Discipline: Mathematics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): Polish groups Graev metrics topological similarity induced conjugacy classes Urysohn space
Abstract: There are two main topics in the thesis. In the second chapter we study two-dimensional classes of topological similarity in the groups of automorphisms of some linearly ordered Fraisse classes: the rationals, the linearly ordered random graph and the linearly ordered Urysohn space. The main theorem establishes meagerness of two-dimensional similarity classes in these groups. As a byproduct we get some results about the group of isometries of the Urysohn space. The third chapter is devoted to the metrics on the free products and HNN extensions of groups with two-sided invariant metrics. Using the approach of Graev to metrics on the free groups we show the existence of the coproducts in the category of groups with two-sided invariant metrics and Lipschitz homomorphisms. We then apply this theory to formulate a criterion when two topologically similar elements in a SIN Polish group are conjugate inside a bigger SIN Polish group.
Issue Date: 2012-05-22
Rights Information: Copyright 2012 Kostyantyn Slutskyy
Date Available in IDEALS: 2012-05-22
Date Deposited: 2012-05

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