Abstract
Abstract ‘A Decomposition That Does Not Shrink’ gives a nontrivial example of a decomposition of the 3-sphere such that the corresponding quotient space is not homeomorphic to the 3-sphere. The decomposition in question is called the Bing-2 decomposition. Similar to the Bing decomposition from the previous chapter, it consists of the connected components of the intersection of an infinite sequence of nested solid tori. However, unlike the Bing decomposition, the Bing-2 decomposition does not shrink. This indicates the subtlety of the question of which decompositions shrink. The question of when certain decompositions of the 3-sphere shrink is central to the proof of the disc embedding theorem.
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