Homology of linear groups
type: Item
instance of: scholarly article
title: Homology of linear groups
zbMATH Open document ID: 0997.20045
author: Kevin P. Knudson
published in: Progress in Mathematics
publication date: 2001-01-07T00:00:00Z
review text: This monograph gives a survey of the work related to homology of linear groups starting with Quillen's computation of the K-groups of finite fields and Borel's computation of the stable real cohomology of arithmetic groups. The book discusses étale K-theory, homology stability theorems, scissors congruence groups, Suslin's Bloch group, action of \(\text{SL}_2(R)\) on trees for various \(R\), the Friedlander-Milnor conjecture concerning the homology of algebraic groups made discrete, and more. It is a rich source of information. The proofs tend to be sketchy, so that one may have to go back to the sources. For instance, consider the purported inductive proof of our connectedness theorem for posets of unimodular rows. One looks in vain for the smallest poset for which 1-connectedness is actually proved, rather than reduced to 1-connectedness of a smaller poset.
reviewed by: Wilberd van der Kallen
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 20-02
Mathematics Subject Classification ID: 19-02
Mathematics Subject Classification ID: 19B14
zbMATH DE Number: 1548761
zbMATH Keywords: homology of linear groups
zbMATH Keywords: cohomology of arithmetic groups
zbMATH Keywords: K-groups
zbMATH Keywords: K-theory
zbMATH Keywords: homology of algebraic groups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1548761