Neumann, F. orcid.org/0000-0001-9684-2488 and Szymik, M. orcid.org/0000-0002-7078-2699 (2024) Preludes to the Eilenberg–Moore and the Leray–Serre spectral sequences. Documenta Mathematica, 29 (6). pp. 1319-1339. ISSN 1431-0635
Abstract
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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2024 The Authors. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematical and Physical Sciences |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 21 Jan 2025 14:41 |
Last Modified: | 21 Jan 2025 14:41 |
Published Version: | https://doi.org/10.4171/dm/978 |
Status: | Published |
Publisher: | European Mathematical Society - EMS - Publishing House GmbH |
Refereed: | Yes |
Identification Number: | 10.4171/dm/978 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:222036 |