A method for shrinking decompositions of certain manifolds

Robert D. Edwards, Leslie C. Glaser
1972 Transactions of the American Mathematical Society  
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
more » ... ut 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.
doi:10.1090/s0002-9947-1972-0295357-6 fatcat:vp5ovfic7vatfon6lbdggjtkkq