Timeline for The cone on a manifold
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| Nov 2, 2013 at 1:15 | comment | added | Jason DeVito - on hiatus | One the other hand, the double suspension of a homology sphere is homeomorphic to a sphere. So the cone of a non-manifold can be a manifold. See J. W. Cannon: Shrinking cell-like decompositions of manifolds. Codimension three, Ann. Math. 110 (1979), 83-112. R. D. Edwards: The double suspension of a certain homology 3-sphere is S^5, Notices AMS 22 (1975), A-334. for details. | |
| Nov 1, 2013 at 17:29 | comment | added | Oscar Randal-Williams | @user40911 Not in high dimensions: if $C\Sigma$ had a smooth structure for which $\Sigma \hookrightarrow C\Sigma$ were a smooth embedding, then removing a small ball from $C\Sigma$ we obtain an $h$-cobordism from $\Sigma$ to the sphere, so $\Sigma$ is not exotic. | |
| Nov 1, 2013 at 16:29 | comment | added | user126154 | Is it true that, under smoothness assupmtion, X is diffeomorphic to a sphere? (I'm not a specialist, but for instance, if I take the cone of an exotic 7-sphere, does it admit a smooth structure?) | |
| Nov 1, 2013 at 15:30 | history | answered | Sam | CC BY-SA 3.0 |