## New answers tagged group-cohomology

1
vote

Accepted

### Groups homology with coefficients fitting into filtration or exact sequence

Think of your exact sequence as a resolution of $M_m$. It's not necessarily a resolution by free $G$-modules, or by projective $G$-modules; it's just a resolution by $G$-modules. You get a spectral ...

1
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### Classification of crossed $G$-algebras

This is an answer to a question posed in the comments, not an answer to the original question. (Too long to fit comfortably as a comment.)
Given a surface $Y$ (e.g. annulus or pair-of-pants), let $R(...

2
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### Classification of crossed $G$-algebras

The classification of 2-dimensional TQFTs with G-action that I'm familiar with goes as follows. Such TQFTs are equivalent to (1) a module category for the tensor category $Vec_G$; or, equivalently, (...

7
votes

Accepted

### Cohomologically trivial module $M$ such that $M/pM$ is not cohomologically trivial for some $p\in\mathbb{N}$

For $n=p$ an odd prime, $M=\mathbb Z/p^2$, where a generator of $\mathbb Z/p$ acts by multiplication by $1+p$, is an example.
$M/pM$ is $\mathbb Z/p$ with the trivial action of $\mathbb Z/p$, which ...

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