A derived functor approach to bounded cohomology
type: Item
instance of: scholarly article
title: A derived functor approach to bounded cohomology
zbMATH Open document ID: 1148.18007
author: Theo Bühler
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2008-06-26T00:00:00Z
review text: The author applies some results about derived categories to the category of Banach modules over a discrete group \(G\), \(G\)-\({\mathcal B}an\). Since this category has enough injective objects, its derived category \({\mathcal D}({\mathcal B}an)\) exists and its heart is equivalent to the category of quotient Banach spaces \(q{\mathcal B}an\). Therefore, a universal \(\delta\)-functor \(\mathcal{H}^{n}:G\)-\({\mathcal B}an\to q{\mathcal B}an\) exists and this is used in Theorem 4.1 to reconstruct the bounded cohomology functors in the sense of Gromov-Brooks-Ivanov-Noskov.
reviewed by: Simion Sorin Breaz
Mathematics Subject Classification ID: 18G10
Mathematics Subject Classification ID: 18E30
zbMATH DE Number: 5293449
zbMATH Keywords: derived category
zbMATH Keywords: Banach module
zbMATH Keywords: bounded cohomology
MaRDI profile type: Publication
full work available at URL: j.crma.2008.04.003
OpenAlex ID: W2087959688
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DOI: 10.1016/J.CRMA.2008.04.003
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description: scientific article; zbMATH DE number 5293449