A closed model category for ()-connected spaces

For each integer , we give a distinct closed model category structure to the category of pointed spaces such that the corresponding localized category is equivalent to the standard homotopy category of -connected CW-complexes. The structure of closed model category given by Quillen to is based on maps which induce isomorphisms on all homotopy group functors and for any choice of base point. For each , the closed model category structure given here takes as weak equivalences those maps that for the given base point induce isomorphisms on for .