University of Illinois Urbana-Champaign

Extending partial isomorphisms

Slutskyy, Kostyantyn

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Slutskyy_Kostyantyn.pdf

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https://hdl.handle.net/2142/30971

Description

Title
Extending partial isomorphisms
Author(s)
Slutskyy, Kostyantyn
Issue Date
2012-05-22T00:19:13Z
Director of Research (if dissertation) or Advisor (if thesis)
Rosendal, Christian
Doctoral Committee Chair(s)
van den Dries, Lou
Committee Member(s)
  • Solecki, Slawomir
  • Rosendal, Christian
  • Kapovitch, Ilia
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2012-05-22T00:19:13Z
Keyword(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.
Graduation Semester
2012-05
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http://hdl.handle.net/2142/30971
Copyright and License Information
Copyright 2012 Kostyantyn Slutskyy

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