2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65020The disk embedding lemma is a technique underlying the topological classification results in 4-manifold topology for good fundamental groups. The purpose of this paper is to develop new tools for disk embedding that work up to s-cobordism, without restrictions on the fundamental group. As an application we show that a surgery problem gives rise to a collection of capped gropes that fit in the framework of control theory.11 pages, 6 figuresGeometric Topologytext