Homology of linear groups
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.
scientific article; zbMATH DE number 1548761
scientific article