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 ${S^3}$.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 289 (1985), 227-252
- MSC: Primary 57N10; Secondary 54B10, 57N30, 57N60
- DOI: https://doi.org/10.1090/S0002-9947-1985-0779062-4
- MathSciNet review: 779062