Kulagin V. Orbit properties pseudo-homeomorphism groups of Polish spaces

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0402U000368

Thesis Registration Form

0402U000368.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

25-12-2001

Specialized Academic Board

Д 64.175.01

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine

Essay

Pseudo-homeomorphism groups of Polish spaces. To classify equivalence relations generated by pseudo-homeomorphism groups, their cocycles, subrelations and automorphisms. Methods of research are methods of ergodic theory and functional analysis. A complete classification of generic nonergodic equivalence relations is obtained; the uniqueness theorem for ergodic cocycles is proved; the notion of topological Mackey action is introduced; regular and transient cocycles are classified; normal and finite index subrelations are classified; the outer conjugacy problem for automorphism groups of generic equivalence relation is solved. Fields of employment are theory of topological dynamical systems, C*-algebra theory.

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