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Shrinking of toroidal decomposition spaces

Daniel Kasprowski, Mark Powell (2014)

Fundamenta Mathematicae

Given a sequence of oriented links L¹,L²,L³,... each of which has a distinguished, unknotted component, there is a decomposition space 𝓓 of S³ naturally associated to it, which is constructed as the components of the intersection of an infinite sequence of nested solid tori. The Bing and Whitehead continua are simple, well known examples. We give a necessary and sufficient criterion to determine whether 𝓓 is shrinkable, generalising previous work of F. Ancel and M. Starbird and others. This criterion...

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