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Architecture of Infinite Towers and Skyscrapers

Architecture of Towers and Skyscrapers formalizes the results from the previous chapter, regarding the structure of gropes and towers, and establishes the notation used for towers and skyscrapers in the remainder of the book. In particular, the boundaries of towers and skyscrapers are carefully described. The boundaries are divided into subsets called the floor, the walls, and the ceiling, and the topology of each of them is identified. The walls are associated with certain mixed Bing–Whitehead decompositions from a previous chapter. How the endpoint compactification of a tower corresponds to a quotient space with respect to a decomposition is also described.