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Transactions of the American Mathematical Society

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



A method for shrinking decompositions of certain manifolds

Authors: Robert D. Edwards and Leslie C. Glaser
Journal: Trans. Amer. Math. Soc. 165 (1972), 45-56
MSC: Primary 57A30
MathSciNet review: 0295357
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Abstract: A general problem in the theory of decompositions of topological manifolds is to find sufficient conditions for the associated decomposition space to be a manifold. In this paper we examine a certain class of decompositions and show that the nondegenerate elements in any one of these decompositions can be shrunk to points via a pseudo-isotopy. It follows then that the decomposition space is a manifold homeomorphic to the original one. As corollaries we obtain some results about suspensions of homotopy cells and spheres, including a new proof that the double suspension of a Poincaré 3-sphere is a real topological 5-sphere.

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Keywords: Decompositions of manifolds, upper semicontinuous decomposition, radial engulfing, shrinkable, pseudo-isotopy, Poincaré sphere, homotopy manifold
Article copyright: © Copyright 1972 American Mathematical Society