On the algebraic K-theory of \({\mathbb{Z}}\)
type: Item
instance of: scholarly article
title: On the algebraic K-theory of \({\mathbb{Z}}\)
zbMATH Open document ID: 0658.18006
DOI: 10.1016/0022-4049(88)90077-1
author: Dominique Arlettaz
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: The author studies the relationships between \(K_ i{\mathbb{Z}}\), \(H_ i(St({\mathbb{Z}}),{\mathbb{Z}})\), and \(H_ i(SL({\mathbb{Z}}),{\mathbb{Z}})\) for \(i=4\), 5 \((St({\mathbb{Z}})=stabilized\) Steinberg group). He proves that the Hurewicz map \(K_ i{\mathbb{Z}}\to H_ i(St({\mathbb{Z}}))\) is an isomorphism for \(i=4\) and has a cokernel of order 2 for \(i=5\). His main tools include th Hochschild-Serre spectral sequence and an analysis of the spaces \(BSt({\mathbb{Z}})^+\), \(BSL({\mathbb{Z}})^+\) and \(BSL({\mathbb{F}}_ 3)^+\).
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 55R35
zbMATH DE Number: 4075365
zbMATH Keywords: plus-construction
zbMATH Keywords: classifying spaces of discrete groups
zbMATH Keywords: stabilized Steinberg group
zbMATH Keywords: Hurewicz map
zbMATH Keywords: Hochschild-Serre spectral sequence
reviewed by: Michael R. Stein
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90077-1
OpenAlex ID: W2016375330
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description: scientific article; zbMATH DE number 4075365