Math 598, Profinite Groups and Group Cohomology.
Time: T/Th 1030-1145
Location: MATH 215
Homework: Random suggested problems not to be graded.
The suggested textbooks are
(1) Wilson, Profinite Groups
(2) Ribes-Zalesskii, Profinite Groups
The course will cover the following topics (with possibly some additional material)
- Profinite Groups. We will develop the basic theory of profinite groups and profinite completions.
- Group Cohomology. We will develop the basics of group cohomology.
- Various topics.
The lecture notes and any other material needed in the class can be found in the file list below. There is also a list of the material covered in each lecture just below as well:
- January 12. Lecture 1, Topological Spaces.
- January 14. No class.
- January 19. Lecture 2, Filters and Product Spaces.
- January 21. Lecture 3, Inverse Limits.
- January 26. Lecture 4, Profinite Groups.
- January 28. Lecture 5, Completions of Groups.
- February 2. Lecture 6, The Completion of Z.
- February 4. No class (admin day).
- February 9. Lecture 7, Free Groups and Presentations.
- February 11. Lecture 8, Finitely Generated Groups and Subgroups.
- February 16, Lecture 9, Automorphism Groups.
- February 18. No class (admin day).
- February 23, Lecture 10, Rigidity.
- February 25. No class (snow day)
- March 1. No class (Ben is away).
- March 3. Lecture 12, Products of Representations (Ryan will lecture).
- March 8. No class (Ben sick)
- March 10. Lecture 11, Rigidity Continued.
- March 15, March 17. No class (spring break)
- March 22. Lecture 13, Semidirect Products and Group Extensions.
- March 24, Lecture 14, Group Cohomology With Abelian Coefficients.
- March 29. No class (admin day).
- March 31, Lecture 15. Projective Resolutions.
- April 5, Lecture 16. Inflation and the Inflation-Restriction Sequence.
- April 7, Lecture 17. Cup Product.
- April 12, Lecture 18. Cohomology of Profinite Groups. Basics.
- April 14, No class.
- April 19, Lecture 19. Direct Limits and Cohomology.
- April 21, Lecture 20. More Diagrams and Twisting.