2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225693A new type of Hopf invariant is described for the fiber of the pinch map from the mapping cone of a map from A to X onto to the suspension of A; this is then used to study the boundary map in the fibration sequence of Cohen, Moore and Neisendorfer in the case that the mapping cone is an odd dimensional Moore space. The components of the boundary map are then shown to be compatible with Hopf invariants and a filtered splitting of the loops on the fiber is obtained.This is the version published by Geometry & Topology Monographs on 22 2008Algebraic Topology55P99, 55Q20, 55Q25text