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Results tagged with group-cohomology
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user 343
In mathematics, group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G-module M to elucidate the properties of the group.
5
votes
Why aren't there more classifying spaces in number theory?
I suppose we should also mention algebraic k-theory. Quillen defined the k-groups as the homotopy groups of certain classifying spaces. For a unital, associative ring $R$,
$$
K_n(R):=\pi_n(BGL(R)^+), …
- 1,422
3
votes
3
answers
1k
views
Another group cohomology cup product question
I am wondering if there is a way to see the cup product, in some cases, without using cochain complexes. The situation I am interested in is the following:
Let $G=F/R$ be a finitely presented group a …
- 1,422
17
votes
Intuition for Group Cohomology
I'm not sure if this is what you're looking for, but I always think of group (co)homology in terms of the homology of the classifying space for your group. Assuming $G$ is discrete, then there is a to …
- 1,422
22
votes
7
answers
3k
views
Essential theorems in group (co)homology
I'm trying to fill in the gaps in my understanding of group (co)homology and I'm wondering what are considered the "must know" theorems and concepts. I'm thinking of things along the lines of
Hopf' …