A CLOSED MODEL CATEGORY FOR (N-1)-CONNECTED SPACES

For each integer n > 0, we give a distinct closed model category struc ture to the category of pointed spaces Top, such that the correspondin g localized category Ho(Top()(n)) is equivalent to the standard homot opy category of (n - 1)-connected CW-complexes. The structure of close d model category given by Quillen to Top() is based on maps which ind uce isomorphisms on all homotopy group functors pi(q) and for any choi ce of base point. For each n > 0, the closed model category structure given here takes as weak equivalences those maps that for the given ba se point induce isomorphisms on pi(q) for q greater than or equal to n .