MTG7397 Adv Topics Topology II, COHOMOLOGY OF GROUPS
Text:
“Cohomology of Groups” by Kenneth Brown
Schedule and Room:
MWF 6 LIT 205
Grading:
50%Presentation+50%Final; A if >85, B+ if > 80, B if > 70, C+ if > 65, C if > 50, D+ if >40, D if >30.
One in class presentation, the home-taken Final
.Extra credit: up to 10 pts for extra presentation in class, up to 5 pts for solving a * rated problem.
Attendance is strictly recommended.
Office Hours:
MW7 LIT 424
Description of the Course:
January-2025 (Chapters I-II)
- Basics of Homological Algebra
- Homology of Groups
- Hopf’s Theorem
- Homology of Amalgamated Product
February and March before the Spring break (Chapters III, V)
- Homology and cohomology with coefficients
- Tor and Ext
- Injective modules
- Induced and coinduced modules
- Shapiro Lemma
- Dimension shifting
- Transfer map
- Cup and cap product
- Pontryagin Product
- Berstein-Schwarz class
- Universality theorem
March after Spring break and April (Chapter VIII)
- Cohomological dimension
- Serre’s theorem
- Resolutions of finite type
- Duality groups
- Virtual Notions
· Presentations, and Extra Credit
· FINAL
· Solutions to the Final
· Announcements
Statement:
· Students requesting classroom accommodation must first register with the Dean of Students Office. The Dean of Students Office will provide documentation to the student who must then provide this documentation to the Instructor when requesting accommodation.