Preludes to the Eilenberg-Moore and the Leray-Serre spectral sequences

Frank Neumann; Markus Szymik

doi:10.4171/dm/978

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arXiv · 2106.10209

Preludes to the Eilenberg-Moore and the Leray-Serre spectral sequences

Frank Neumann·Markus Szymik

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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.

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BibTeX RIS

Frank Neumann, Markus Szymik. 2021-06-18. Preludes to the Eilenberg-Moore and the Leray-Serre spectral sequences. https://doi.org/10.4171/dm/978

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