Context for the Disc Embedding Theorem

‘Context for the Disc Embedding Theorem’ explains why the theorem is the central result in the study of topological 4-manifolds. After recalling surgery theory and the proof of the s-cobordism theorem for high-dimensional manifolds, the chapter explains what goes wrong when trying to apply the same techniques in four dimensions and how to start overcoming these problems. The complete statement of the disc embedding theorem is provided. Finally the most important consequences to manifold theory are listed, including a proof of why Alexander polynomial one knots are topologically slice and the existence of exotic smooth structures on 4-dimensional Euclidean space.