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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


  •  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.


  1. Topological groups; definition and basic properties, subgroups, quotient groups, examples; direct and semidirect product of groups
  2. Transformation groups; definition, examples, isotropy groups, orbits, orbit spaces, fixed point sets, equivariant mappings
  3. Actions of compact groups and proper actions of locally compact groups
  4. Applications to the theory of covering spaces
  5. Haar integral; the Tietze-Gleason theorem, invariant metrics
  6. Slices and twisted products, fundamental sets.


One exam at the end of the course: Wednesday 21.12. at 10-14, classroom B322.

Course material

Chapter I: Luku1.pdf

Chapter II: Luku2.pdf

Chapter III: Luku3.pdf

Chapter IV: Luku4.pdf

Chapter V: Luku5.pdf

Chapter VI: Luku6.pdf

Appendix A, On paracompactness: A.pdf

Appendix B, Nets in topology: B.pdf

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


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Exercise classes

1.Thursday 12-14 C122 Erik Elfving 

Course feedback

Course feedback can be given at any point during the course. Click here.

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