1
vote
0answers
75 views

Can group cohomology be used to study fiber bundles?

Is (non-abelian) cohomology used to study vector and principal bundles? Can you give me a text or an article? For example: Consider a vector bundle $E$ with fiber $V$ and base manifold $M$. Consider ...
5
votes
1answer
59 views

Reference request: Introduction to Finite Group Cohomology

I don't know anything about group cohomology and I'd like to. What is the best text to learn this subject? I'd prefer as soft an introduction as possible - that is, lots of motivation, lots of ...
4
votes
2answers
231 views

Motivation for Schur multipliers

What are Schur multipliers good for? I should probably clarify what I want. Here is an instructive story of how I came to appreciate complex representations and characters of groups. Basically, I ...
3
votes
1answer
95 views

Schur multiplier of the symmetric group

It is known that $H^2(S_n, \mathbb{C}^\times) \cong \mathbb{Z}/2\mathbb{Z}$ for $n \geq 4$. Is an explicit formula as a function $S_n \times S_n \to \mathbb{C}^\times$ for a representative of the ...
4
votes
1answer
468 views

Exercises in Group Cohomology

I'm interested in finding a textbook to learn group cohomology, a book that contains a lot of examples and also a lot of good exercises to test my understanding. I would appreciate some feedback. ...
5
votes
0answers
162 views

Dual modules and first cohomology

Let $G$ be a finite group, $K$ a characteristic-$p$ algebraically closed field (say $p$ divides $|G|$), and let $M$ be a finite-dimensional $KG$-module. What hypotheses are needed on $G$, $M$ to ...