Spring 2016: Math 598, Profinite Groups and Group Cohomology

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)

  1. Profinite Groups. We will develop the basic theory of profinite groups and profinite completions.
  2. Group Cohomology. We will develop the basics of group cohomology.
  3. 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.