Skip to main content

All Questions

Filter by
Sorted by
Tagged with
13 votes
2 answers
929 views

Group cohomology without G-modules (a.k.a. what does this bar construction compute?)

Without any prior exposure to the cohomology of groups, one might naively proceed by replacing a group by a sort of resolution. For instance, let's take $G = \mathbb{Z}^2$, and "resolve": $$ 0 \to \...
Will's user avatar
  • 805
7 votes
0 answers
178 views

Stabilisation of crossed modules?

D. Conduché has introduced a notion of a stable crossed module ("Modules croisés généralisés de longueur 2", JPAA 34 (1984) pp155–178, doi:10.1016/0022-4049(84)90034-3, Def. 3.1). Is there a ...
Matthias Künzer's user avatar
3 votes
0 answers
189 views

Geometric realization of crossed square

Given a crossed square of groups, you can "totalize" it and get a 2 crossed module in the sense of Conduché "Modules croisés généralisés de longueur 2", then you can apply his ...
clovis chabertier's user avatar
3 votes
0 answers
94 views

Explicit examples of 4-cocycles over finite 2-groups

By a (finite) 2-group $X$, I mean a finite group $G$, a finite abelian group $A$, an action of $G$ on $\operatorname{Aut}(A)$, as well as a 3-cocycle $\alpha\in H^3(BG, A)$. They are also equivalent ...
Andi Bauer's user avatar
  • 3,001