A nonshrinkable decomposition of 𝑆³ whose nondegenerate elements are contained in a cellular arc

Row, W. H.; Walsh, John J.

doi:10.1090/S0002-9947-1985-0779062-4

A nonshrinkable decomposition of $S^ 3$ whose nondegenerate elements are contained in a cellular arc
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by W. H. Row and John J. Walsh PDF

Trans. Amer. Math. Soc. 289 (1985), 227-252 Request permission

Abstract:

A decomposition $G$ of ${S^3}$ is constructed with the following properties: (1) The set ${N_G}$ of all nondegenerate elements consists of a null sequence of arcs and $J = {\text {CL}}( \cup \{ g \in {N_G}\} )$ is a simple closed curve. (2) Each arc contained in $J$ is cellular. (3) $J$ is the boundary of a disk $Q$ that is locally flat except at points of $J$. (4) The decomposition $G$ is not shrinkable; that is, the decomposition space is not homeomorphic to ${S^3}$.

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