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Results tagged with group-cohomology
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user 4991
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.
19
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2
answers
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Geometric model for classifying spaces of alternating groups
The classifying space of the nth symmetric group $S_n$ is well-known to be modeled by the space of subsets of $R^\infty$ of cardinality $n$. Various subgroups of $S_n$ have related models. For examp …
- 4,990
12
votes
Why aren't there more classifying spaces in number theory?
As a topologist, my view is that group cohomology of interest to number theorests seems to generally be with non-trivial module coefficients. Many of the tricks topologists employ to study spaces do …
- 4,990
8
votes
Essential theorems in group (co)homology
Here's one which is key for calculations: Let $H$ be a subgroup of $G$ and $W_G(H) = N_G(H)/H$. Then the restriction map $H^*(BG) \to H^*(BH)$ maps to the invariants $(H^*(BH))^{W_G(H)}$.
When $H$ …
8
votes
Accepted
Characteristic classes of symmetric group $S_4$
For Q2, my collaborators and I show that all mod-two cohomology of symmetric groups is generated by Stiefel-Whitney classes of standard representations, if you allow both cup product and transfer (ind …
- 4,990