A method for shrinking decompositions of certain manifolds

Edwards, Robert D.; Glaser, Leslie C.

doi:10.1090/S0002-9947-1972-0295357-6

A method for shrinking decompositions of certain manifolds
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by Robert D. Edwards and Leslie C. Glaser PDF

Trans. Amer. Math. Soc. 165 (1972), 45-56 Request permission

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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