Group Cohomology

Group cohomology is the application of cohomological algebra to group theory. We can define spaces that encode all the information of a group and then apply the cohomological constructions from topology to these spaces, or we can equivalently form this construction abstractly using only group theory. We will be sticking to Kenneth Brown’s text, ‘Cohomology of Groups’.
 
Organizer: Sean O’Brien
When: Thursday 9am – 11am
Where: Room 309, mathematics and statistics building, Glasgow, and online on request.
(Not in that room on December 18th, will book somewhere closer to that date)

 

Schedule: 

    1. 2025-10-09, Chapter 1.0-1.3 Review of chain complexes, free resolutions, group rings, G -modules: Sean O’Brien.
        • The notes go further than I did on the day.
    2. 2025-10-16, Chapter 1.4-1.6 Resolutions of Z over ZG, The standard resolution: Susanna Terron
    3. 2025-10-23, Chapter 1.7-2.4 Uniqueness of Resolutions, Projective modules, Homology of groups: Zoltán Lelkes

Lecture notes: