Timeline for Are there non-smoothable homotopy/homology spheres?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 14, 2016 at 19:12 | vote | accept | Michael Albanese | ||
| Apr 13, 2016 at 21:32 | history | edited | Michael Albanese | CC BY-SA 3.0 |
deleted 12 characters in body
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| Apr 13, 2016 at 21:31 | comment | added | Michael Albanese | @QiaochuYuan: You're right, that is a more natural definition and it seems to be the one that others use. I will edit accordingly. | |
| Apr 13, 2016 at 21:07 | comment | added | Qiaochu Yuan | I'm a little confused about this definition of homotopy sphere. Surely what you want is a manifold homotopy equivalent to the sphere? I think your definition happens to be equivalent, but in a somewhat indirect way, which seems a little misleading. | |
| Apr 13, 2016 at 1:22 | answer | added | Igor Belegradek | timeline score: 26 | |
| Apr 12, 2016 at 20:37 | comment | added | Qiaochu Yuan | @Mariano: presumably it means homeomorphic to the usual sphere. | |
| Apr 12, 2016 at 20:16 | comment | added | Mariano Suárez-Álvarez | What does "topologically standard" mean? | |
| Apr 12, 2016 at 19:19 | comment | added | Ryan Budney | I suppose it depends on what you call smoothing theory. The transition from topological to PL or smooth structure is what I'm calling smoothing theory. You don't need the full machine at this step, but you need the basics of it. | |
| Apr 12, 2016 at 19:16 | comment | added | mme | @RyanBudney In high dimensions it should be easier than smoothing theory, because homotopy spheres are all topologically standard, no? | |
| Apr 12, 2016 at 18:47 | comment | added | Ryan Budney | I believe the answer is no for homotopy spheres, although I won't be able to assemble all the references here. In dimension 3 and below it's classical all manifolds can be smoothed. In dimension 4 it follows by Freedman's work -- the smoothing obstruction requires some homology to exist. In high dimensions it pops out of smoothing theory... but precisely who to credit or where to look I am uncertain. I would strongly suspect Kirby and Siebenmann being responsible for this. For homology spheres I believe the answer is yes, and there are some classical low-dimensional examples. | |
| Apr 12, 2016 at 18:26 | history | asked | Michael Albanese | CC BY-SA 3.0 |