It is a well known that in case when we have $\xi: E\to B$ - a Serre fibration, with the trivial action of $\pi_1(B)$ on a fiber $F$, we have standart Atiyah - Hirzebruch spectral sequence. What we have in the case when $\pi_1(B)$ acts non-trivially? Please, give me some links to the subject.
Spectral sequence of non-cohomologically trivial fibration.
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algebraic-topology
spectral-sequences
fibration
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0You need local coefficients. See [the first section here](https://arxiv.org/pdf/1005.0379.pdf). – 2017-01-02
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0Great link, thank you very much! – 2017-01-03