The third homology of the special linear group of a field

We prove that for any infinite field F, the map H-3(SLn(F), Z) -> H-3(SLn+1 (F), Z) is an isomorphism for all n >= 3. When n = 2 the cokernel of this map is naturally isomorphic to 2. K-3(M) (F), where K-n(M)(F) is the nth Milnor K-group of F. We deduce that the natural homomorphism from H-3(SL2(F), Z) to the indecomposable K-3 of F, K-3(F)(ind), is surjective for any infinite field F.Science Foundation Irelan