Cohomology of Lie groups made discrete (Q753210)

Let G be a Lie group, and let \(G^{\delta}\) denote the same group with the discrete topology. A conjecture of E. Friedlander and J. Milnor says that the mapping \(\eta\) : BG\({}^{\delta}\to BG\) between classifying spaces induced by the identity map \(G^{\delta}\to G\) induces isomorphisms on homology and cohomology with finite coefficients. The problem of computing the (co)homology of \(BG^{\delta}\) arises among others in the theory of foliations and in algebraic K-theory. The paper under review gives a survey of results due to Milnor, Friedlander, Mislin, Suslin, Sah, and others related with the conjecture.