Director of Research (if dissertation) or Advisor (if thesis)
Tserunyan, Anush
Doctoral Committee Chair(s)
Solecki, Sławomir
Committee Member(s)
Albin, Pierre
Oikhberg, Timur
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
Generic Elements
Conjugacy Classes
Automorphism Groups
Random Poset
Absolutely Continuous
Topological Rank
Language
eng
Abstract
For a Polish group G, we say an element g ∈ G is generic if it has a comeagre conjugacy class. We examine the questions of existence, and of behavior, for generic elements in two particular Polish groups. Firstly, we give a concrete model-theoretic characterization of the generic automorphism of the countable universal ultrahomogeneous partial order, also called the random poset. Secondly, we prove that the group of order-preserving, absolutely continuous homeomorphisms of the interval admits generic elements, and we give a concrete characterization. Additionally, we show that this group is generically topologically 2-generated; that is, for a comeagre set of pairs (f,g) of absolutely continuous interval homeomorphisms, the subgroup is dense.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
