Suspensions of homology spheres

This article is one of three highly influential articles on the topology of manifolds written by Robert D. Edwards in the 1970’s but never published. This article “Suspensions of homology spheres” presents the initial solutions of the fabled Double Suspension Conjecture. The article “Approximating certain cell-like maps by homeomorphisms” presents the definitive theorem on the recognition of manifolds among resolvable generalized manifolds. (This work garnered Edwards an invitation to give a one-hour plenary address to the 1978 International Congress of Mathematicians.) The third article “Topological regular neighborhoods” develops a comprehensive theory of regular neighborhoods of locally flatly embedded topological manifolds in high dimensional topological manifolds. The manuscripts of these three articles have circulated privately since their creation. The organizers of the Workshops in Geometric Topology (http://www.math.oregonstate.edu/ ̃topology/workshop.htm) with the support of the National Science Foundation have facilitated the preparation of electronic versions of these articles to make them publicly available. This article contains four major theorems: I. The double suspension of Mazur’s homology 3-sphere is a 5-sphere, II. The double suspension of any homology n-sphere that bounds a contractible (n+1)-manifold is an (n+2)-sphere, III. The double suspension of any homology 3-sphere is the cell-like image of