Key Facts about Skyscrapers and Decomposition Space Theory

‘Key Facts about Skyscrapers and Decomposition Space Theory’ summarizes the input from Parts I and II needed for the remainder of the proof of the disc embedding theorem. Precise references to previous chapters are provided. This enables Part IV to be read independently from the previous parts, provided the reader is willing to accept the facts from Parts I and II summarized in this chapter. The listed facts include the shrinking of mixed, ramified Bing–Whitehead decompositions of the solid torus, the shrinking of null decompositions consisting of recursively starlike-equivalent sets, the ball to ball theorem, the skyscraper embedding theorem, and the collar adding lemma.