Serre homotopy theory in subcategories of simplicial groups (Q1973359)

The authors develop a closed model structure for simplicial groups which are reduced up to some fixed degree \(r\) and then trivial in homotopy group beyond some higher degree \(n\). The weak equivalences for the theory are maps \(G \rightarrow H\) which induce isomorphisms \(S^{-1}\pi_{\ast}G \rightarrow S^{-1}\pi_{\ast}H\) for some multiplicative subset \(S\) of the integers, and the fibrations are the \(S\)-fibrations in the sense of Quillen in the larger category of \(r\)-reduced simplicial groups. The authors give, in effect, rational homotopy style model structures for highly connected Postnikov sections, but no concrete applications are mentioned.