Finite-dimensional spaces in resolving classes

摘要

Using the theory of resolving classes, we show that if X is a CW complex of finite type such that map~*(X, S ~2n+1) ~(～ *) for all suficiently large n, then map~*(X;K) ~(～ *) for every simply-connected finite-dimensional CW complex K; and under mild hypotheses on π1(X), the same conclusion holds for all finite-dimensional complexes K. Since it is comparatively easy to prove the former condition for X = BZ=p (we give a proof in an appendix), this result can be applied to give a new, more elementary proof of the Sullivan conjecture.