Suspensions of homology spheres
Abstract
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. It presents the initial solutions of the fabled Double Suspension Conjecture. (The other two articles are: 'Approximating certain celllike maps by homeomorphisms' and 'Topological regular neighborhoods') 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. The second and third articles are still in preparation. The current article contains four major theorems: I. The double suspension of Mazur's homology 3sphere is a 5sphere, II. The double suspension of any homology nsphere that bounds a contractible (n+1)manifold is an (n+2)sphere, III. The double suspension of any homology 3sphere is the celllike image of a 5sphere. IV. The triple suspension of any homology 3sphere is a 6sphere. Edwards' proof of I. was the first evidence that the suspension process could transform a nonsimply connected manifold into a sphere, thereby answering a question that had puzzled topologists since the mid1950's if not earlier. Results II, III and IV represent significant advances toward resolving the general double suspension conjecture: the double suspension of every homology nsphere is an (n+2)sphere. [That conjecture was subsequently proved by J. W. Cannon (Annals of Math. 110 (1979), 83112).]
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2006
 arXiv:
 arXiv:math/0610573
 Bibcode:
 2006math.....10573E
 Keywords:

 Mathematics  Geometric Topology;
 57N15;
 57Q15;
 57P99
 EPrint:
 84 pages, 27 figures