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### 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 ...
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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 $R(... • 12k 2 votes ### Classification of crossed$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$; or, equivalently, (... • 12k 7 votes Accepted ### Cohomologically trivial module$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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