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\(\pi {}_ 1\) 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)