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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A nonshrinkable decomposition of $ S\sp 3$ whose nondegenerate elements are contained in a cellular arc


Authors: W. H. Row and John J. Walsh
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
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0779062-4
Keywords: Cellular decomposition, cellular arc, nonshrinkable, $ 3$-manifold
Article copyright: © Copyright 1985 American Mathematical Society