Geodesic
Preludes to the Eilenberg–Moore and the Leray–Serre spectral sequences
Documenta mathematica, Tome 29 (2024) no. 6, pp. 1319-1339 Cet article a éte moissonné depuis la source EMS Press

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The Leray–Serre and the Eilenberg–Moore spectral sequences are fundamental tools for computing the cohomology of a group or, more generally, of a space. We describe the relationship between these two spectral sequences when both of them share the same abutment. There exists a joint tri-graded refinement of the Leray–Serre and the Eilenberg–Moore spectral sequence. This refinement involves two more spectral sequences, the preludes from the title, which abut to the initial terms of the Leray–Serre and the Eilenberg–Moore spectral sequence, respectively. We show that one of these always degenerates from its second page on and that the other one satisfies a local-to-global property: it degenerates for all possible base spaces if and only if it does so when the base space is contractible.
DOI : 10.4171/dm/978
Classification : 18G40, 55R20, 55T10, 55T20
Mots-clés : spectral sequences, Eilenberg–Moore spectral sequence, Leray–Serre spectral sequence 
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     title = {Preludes to the {Eilenberg{\textendash}Moore} and the {Leray{\textendash}Serre} spectral sequences},
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Frank Neumann; Markus Szymik. Preludes to the Eilenberg–Moore and the Leray–Serre spectral sequences. Documenta mathematica, Tome 29 (2024) no. 6, pp. 1319-1339. doi: 10.4171/dm/978

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