Extending partial isomorphisms

Slutskyy, Kostyantyn

Permalink

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

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

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

Permalink

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

Copyright and License Information

Copyright 2012 Kostyantyn Slutskyy

Owning Collections