Applications of controlled surgery in dimension 4 : examples

The validity of Freedmans disc theorem is known to depend only on the fundamental group.It was conjectured that it fails for non abelian free fundamental groups.If this were true then surgery would work in dimension four.Recently,Krushkal and Lee proved a surprising result that surgery works for a large class of 4-manifolds with free nonabelian fundamental groups.The goal of this paper is to show that this is best understood using controlled surgery theory