On the homology of the special linear group over a number field
type: Item
instance of: scholarly article
title: On the homology of the special linear group over a number field
zbMATH Open document ID: 0621.20028
DOI: 10.1007/BF02621932
author: Dominique Arlettaz
published in: Commentarii Mathematici Helvetici
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140068
review text: Let F be a number field and \(G=SL(F)\) the infinite special linear group over F. The main result of this paper: for all \(i\geq 0\), the i-th homology of G with integral coefficients (which in general is not finitely generated) is the direct sum of a torsion group and a free abelian group of finite rank. This depends on the fact (also proved in this paper) that the Postnikov k-invariants of a connected infinite loop space are cohomology classes of finite order. As an application, the author proves that there exists an integer E depending only on i and F such that for any representation r of any discrete group into GL(F), E times the i-th Chern-class of r equals 0.
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 55P47
Mathematics Subject Classification ID: 55S45
Mathematics Subject Classification ID: 20G30
Mathematics Subject Classification ID: 11R70
zbMATH DE Number: 4006534
zbMATH Keywords: number field
zbMATH Keywords: special linear group
zbMATH Keywords: homology
zbMATH Keywords: Postnikov k-invariants
zbMATH Keywords: connected infinite loop space
zbMATH Keywords: cohomology classes of finite order
zbMATH Keywords: Chern- class
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4006534