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9 votes
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Hochschild-Serre spectral sequence via explicit filtration

Let $$1 \longrightarrow K \longrightarrow G \longrightarrow Q \longrightarrow 1$$ be a short exact sequence of groups and let $M$ be a $\mathbb{Z}[G]$-module. The Hochschild--Serre spectral ...
Laura's user avatar
  • 163
4 votes
0 answers
207 views

Trivial action in the Hochschild-Serre spectral sequence

I probably don't understand something very basic about Hochschild-Serre spectral sequence. Let $G$ be a group with normal subgroup $N$ and $M$ a $G$-module with trivial action. Then as far as I ...
David Levit-Gurevich's user avatar
3 votes
0 answers
149 views

Group cohomology with coefficients in a graded module

I am working in a problem group cohomology and nailed it down to compute a cohomology using an spectral sequence argument. The situation is as follows: Let $G = C_4 = \langle \sigma \rangle$ be the ...
C. Zhihao's user avatar
  • 283
3 votes
0 answers
174 views

Induced Homomorphism on Cohomology of Symmetric Group 3

For the symmetric group $S_3$, there is an inclusion $i:\mathbb{Z}/3\mathbb{Z}\hookrightarrow S_3$. How can I assert that the induced homomorphism $$i^{\ast}:H^{n}(S_3,\mathbb{Z})\rightarrow H^{n}(\...
mrde05's user avatar
  • 39
3 votes
0 answers
120 views

Trivialize a cocycle of a continuous Lie group-cohomology to a coboundary

Someone recently asks a question $SO(3)$ 2-cocycle trivialized to a 2-coboundary in $SU(2)$? now inspires me to revisit an earlier general question to ask an example of 3-cocycle $\omega_3^G$ of a ...
wonderich's user avatar
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