2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223658We present a new property, the Disjoint Path Concordances Property, of an ENR homology manifold X which precisely characterizes when X times R has the Disjoint Disks Property. As a consequence, X times R is a manifold if and only if X is resolvable and it possesses this Disjoint Path Concordances Property.This is the version published by Geometry & Topology Monographs on 22 April 2006Geometric TopologyGeneral Topology57N15, 57P05, 54B15, 57N70, 57N75text