## $$\pi {}_ 1$$ et $$d_ 2$$.(French)Zbl 0548.55014

Homotopie algébrique et algèbre locale, Journ. Luminy/France 1982, Astérisque 113-114, 234-237 (1984).
Summary: [For the entire collection see Zbl 0535.00017.]
Given a bundle $$X\to E\to V$$ with $$\pi_ 1(V)$$ not zero. Besides the monodromy of local systems $$H_*(X)$$ or $$\pi_*(X)$$ associated to E and which appear in the $$E^ 2$$-terms of the Serre spectral sequence (or generalized Shih spectral sequence [see the author, Homotopie des espaces de sections (1982; Zbl 0535.55001)]) the differentials $$d_ 2$$ of these spectral sequences bring us $$\pi_ 1(V)$$ actions on $$H_*(X)$$ or $$\pi_*(x)$$. We explain here these actions.

### MSC:

 55R20 Spectral sequences and homology of fiber spaces in algebraic topology 55R05 Fiber spaces in algebraic topology 55T10 Serre spectral sequences 55N25 Homology with local coefficients, equivariant cohomology 18G40 Spectral sequences, hypercohomology 18G15 Ext and Tor, generalizations, Künneth formula (category-theoretic aspects)

### Citations:

Zbl 0535.00017; Zbl 0535.55001