Geodesic
Preludes to the Eilenberg–Moore and the Leray–Serre spectral sequences
Documenta mathematica, Tome 29 (2024) no. 6, pp. 1319-1339

Voir la notice de l'article provenant de la source EMS Press

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 
@article{10_4171_dm_978,
     author = {Frank Neumann and Markus Szymik},
     title = {Preludes to the {Eilenberg{\textendash}Moore} and the {Leray{\textendash}Serre} spectral sequences},
     journal = {Documenta mathematica},
     pages = {1319--1339},
     publisher = {mathdoc},
     volume = {29},
     number = {6},
     year = {2024},
     doi = {10.4171/dm/978},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/978/}
}
TY  - JOUR
AU  - Frank Neumann
AU  - Markus Szymik
TI  - Preludes to the Eilenberg–Moore and the Leray–Serre spectral sequences
JO  - Documenta mathematica
PY  - 2024
SP  - 1319
EP  - 1339
VL  - 29
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/978/
DO  - 10.4171/dm/978
ID  - 10_4171_dm_978
ER  - 
%0 Journal Article
%A Frank Neumann
%A Markus Szymik
%T Preludes to the Eilenberg–Moore and the Leray–Serre spectral sequences
%J Documenta mathematica
%D 2024
%P 1319-1339
%V 29
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/978/
%R 10.4171/dm/978
%F 10_4171_dm_978
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

Cité par Sources :