NSCPHD1213 Full groups of cantor minimal systems

Volume 2013/2014
Content
Full groups originated in ergodic theory in the work of Henri Dye in the late 50's. Since then similar construction were found to be usefull in many others areas of dynamical systems. The course will focus on the topological full groups of minimal homeomorphisms of the Cantor space.  The following topics will be covered:  spatial realizations of automorphisms between full groups, Boyle's flip conjugacy theorem, commutators of topological full groups, Bratteli diagrams, Vershik maps, finte generation of commutators of topological full groups of minimal subshifts.
Learning Outcome
Students are expected to know the definition and basic properties of topological full group of Cantor minimal systems, to be able to formulate the spatial realization and Boyle's theorem, give examples of Bratteli diagrams and Vershik maps with various properties.
Students are assumed to be familiar with basics of point-set topology: compactness, metrizability, separability, etc. Familiarity with the theory of full groups in ergodic theory will be helpful, but not strictly necessary.
lectures/exercises
  • Category
  • Hours
  • Course Preparation
  • 150
  • Lectures
  • 28
  • Preparation
  • 28
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Marking scale
7-point grading scale
Censorship form
No external censorship
Re-exam
Oral examination, 30 min.
Marking scale: 7-point grading scale. No external censorship, no external examiner.
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.