Tower Height Raising and Embedding

‘Tower Height Raising and Embedding’ shows how to raise the height of towers, as well as how to detect embedded towers within a given tower. Raising the number of storeys of a capped tower by one is a construction similar in spirit to grope height raising, but more sophisticated. The new aspect, which receives careful treatment, is the geometric control needed to make the top storey arbitrarily small. An n-storey capped tower contains a capped tower with (n + 1) storeys and the same attaching region, and this can be realized by an embedding that places connected components of the top storey into balls of arbitrarily chosen small diameter. Consequently, endpoint compactifications of infinite towers may be embedded as well.