On disk embedding up to s-cobordism
  The 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. 
Vyacheslav Krushkal