On the homology of the special linear group over a number field
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.
scientific article; zbMATH DE number 4006534