Subject: homomorphisms from Lie groups to K(Z,3) From: "John Baez" Date: Sun, 20 Mar 2005 19:39:57 -0800 (PST) To: dmd1@lehigh.edu Hi - Suppose G is a simply-connected compact simple Lie group. Then H3(G,Z) = Z and we can represent the generator by a map f: G -> K(Z,3) My question is: can we find a model of K(Z,3) which is an abelian topological group such that f is a homomorphism? I think we can easily do this in an up-to-homotopy sense: represent the generator of H4(BG,Z) by a map g: BG -> K(Z,4) and use Omega(g): Omega(BG) -> Omega K(Z,4) = K(Z,3) together with the homotopy equivalence G ~ Omega(BG). But, for some silly reason I'd like to find an honest homomorphism f: G -> K(Z,3) that does the job, if it's possible. Best, jb