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Shrinking Cell-Like Decompositions of Manifolds. Codimension Three

J. W. Cannon
Annals of Mathematics
Second Series, Vol. 110, No. 1 (Jul., 1979), pp. 83-112
Published by: Annals of Mathematics
DOI: 10.2307/1971245
Stable URL: http://www.jstor.org/stable/1971245
Page Count: 30
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Shrinking Cell-Like Decompositions of Manifolds. Codimension Three
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Abstract

Euclidean n-space $E^n, n \underline {\underline > 5$, has the following simple DISJOINT DISK PROPERTY: singular 2-dimensional disks in En may be adjusted slightly so as to be disjoint. We show that for a large class of cell-like decompositions of manifolds this property in the decomposition space is sufficient in order that the decomposition space be a manifold. As a consequence we deduce the DOUBLE SUSPENSION THEOREM proved in a large number of cases by R. D. Edwards: The double suspension of any homology sphere is a topological sphere. We also obtain a sweeping generalization of Edwards' MANIFOLD FACTOR THEOREM; Edwards' theorem states that, if X is a single cell-like set in Euclidean n-dimensional space En, then (En / E) × E1 = En + 1.

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