Outline of the Upcoming Proof

‘Outline of the Upcoming Proof’ provides a comprehensive outline of the proof of the disc embedding theorem. The disc embedding theorem for topological 4-manifolds, due to Michael Freedman, underpins virtually all our understanding of topological 4-manifolds. The famously intricate proof utilizes techniques from both decomposition space theory and smooth manifold topology. The latter is used to construct an infinite iterated object, called a skyscraper, and the former to construct homeomorphisms from a given topological space to a quotient space. The detailed proof of the disc embedding theorem is the core aim of this book. In this chapter, a comprehensive outline of the proof is provided, indicating the chapters in which each aspect is discussed in detail.