Document

Cohomology of topologised monoids

Title of Periodical
Mathematische Zeitschrift
Issue published
Volume 301, pages 2793–2840, (2022)
Country of Publication
Germany
Place Published
SpringerLink, Berlin, Germany
Publisher
Springer-Verlag GmbH
Date Issued
2022
Language
English
English Abstract
Abstract: We prove standard results of group cohomology – namely, existence of a long exact sequence, classification of torsors via the first cohomology group, Shapiro’s lemma, the Hochschild- Serre spectral sequence, a decomposition of the cochain complex in the direct product case, and Jannsen’s result on the recovery problem – for cohomology theories such as continuous, analytic, bounded, and pro-analytic cohomology. We also prove these results for certain monoids, as the applications we have in mind concern (ϕ, )-modules. The cohomology groups considered here all have very concrete interpretations by means of a cochain complex. Therefore, we do not use methods of homological algebra, but explicit calculations on the level of cochains, using techniques dating back to Hochschild and Serre
Member of
Author's Work
Article
2
Thomas, Oliver
University of Bahrain
2022