Topological transformation groups, fall 2016
Topological transformation groups, fall 2016
Teacher: Erik Elfving
Scope: 10 cr
Type: Advanced studies
Teaching: Four hours of lectures and 2 hours of exercises per week
Topics: Introduction to the theory of topological groups and transformation groups
Prerequisites: Linear algebra and matrices I & II, Topology I & II, Algebra I
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News
- The first meeting is on Monday 5th of September.
- On Wednesday 7th of September there is no meeting, on Thursday 8th of September there is a lecture instead of exercises.
Teaching schedule
Weeks 36-42 and 44-50, Monday 10-12 and Wednesday 14-16 in room C124. Two hours of exercise classes per week.
Contents
- Topological groups; definition and basic properties, subgroups, quotient groups, examples; direct and semidirect product of groups
- Transformation groups; definition, examples, isotropy groups, orbits, orbit spaces, fixed point sets, equivariant mappings
- Actions of compact groups and proper actions of locally compact groups
- Applications to the theory of covering spaces
- Haar integral; the Tietze-Gleason theorem, invariant metrics
- Slices and twisted products, fundamental sets.
Exams
One exam at the end of the course: Wednesday 21.12. at 10-14, classroom B322.
Course material
Chapter I:
Chapter II:
Chapter III:
Chapter IV:
Chapter V:
Chapter VI:
Appendix A, On paracompactness:
Appendix B, Nets in topology:
Auxiliary material:
T. tom Dieck: Transformation groups, Walter de Gruyter, 1987
K. Kawakubo: The theory of transformation groups, Oxford University Press, 1991
S. Illman: Topological transformation groups I & II, lecture notes, 2002-2003
Registration
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Exercises
Assignments
- Exercise 1 (15.9.2016):
- Exercise 2 (22.9.2016):
- Exercise 3 (29.9.2016):
- Exercise 4 (6.10.2016):
- Exercise 5 (13.10.2016):
- Exercise 6 (20.10.2016):
- Exercise 7 (3.11.2016):
- Exercise 8 (10.11.2016):
- Exercise 9 (17.11.2016):
- Exercise 10 (24.11.2016):
- Exercise 11 (1.12.2016):
- Exercise 12 (8.12.2016):
- Exercise 13 (15.12.2016):
Exercise classes
Group | Day | Time | Room | Instructor |
|---|---|---|---|---|
1. | Thursday | 12-14 | C122 | Erik Elfving |
Course feedback
Course feedback can be given at any point during the course. Click here.