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Results tagged with group-cohomology
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user 35575
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.
31
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Why aren't there more classifying spaces in number theory?
Much of modern algebraic number theory can be phrased in the framework of group cohomology. (Okay, this is a bit of a stretch -- much of the part of algebraic number theory that I'm interested in...) …
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9
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Geometric interpretation of the lower central series for the fundamental group?
A special case you might find informative: If $L$ is a link in $S^3$, then Chen-Milnor theory gives you a presentation of the link group $\pi=\pi_1(S^3-L)$ modulo some deeper terms of the the lower c …
- 8,467
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How to fit res map into a long exact sequence?
I think you're looking for the Hochschild-Serre spectral sequence. It's slightly more complicated than a long exact sequence, but you can extract the very concrete "inflation-restriction sequence" ou …
CommunityBot
- 1
9
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Essential theorems in group (co)homology
Shapiro's lemma and dimension-shifting. Cohomology of cyclic groups and Herbrand quotients.
It would be helpful to know what you need to know group cohomology for.
If you have an interest in pr …
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Accepted
Injectivity of Transfer (Verlagerung) map
I'm not sure how to answer the more philosophical question (it's likely you could encode enough of the axioms to force the purely group-theoretic version of the question to be true, but to ask whether …
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9
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Coboundary Representations for Trivial Cup Products
Suppose $G$ is a pro-$p$-group, $p$ odd, and $\mathbb{F}_p$ is given the trivial $G$-action. By skew-symmetry of the cup-product in degree 1, given $\chi\in H^1(G,\mathbb{F}_p)$, we have $\chi\cup\ch …
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