Timeline for History of Poincare conjecture in higher dimension [closed]
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 13, 2015 at 23:31 | history | closed |
HJRW Sam Nead Oscar Randal-Williams Neil Strickland Noah Schweber |
Needs details or clarity | |
| Feb 13, 2015 at 13:41 | answer | added | Sam Nead | timeline score: 5 | |
| Feb 13, 2015 at 10:27 | review | Close votes | |||
| Feb 13, 2015 at 15:25 | |||||
| Feb 13, 2015 at 10:09 | comment | added | HJRW | This question is very unclear. Your 'original' statement of the Poincare Conjecture makes no mention of dimension, but you then write 'Later Poincare conjecture was generalized to the higher dimensions.' Since it is unclear what you are asking, I'm voting to close. (Also, as has been pointed out, in the light of Hurewicz's theorem, the generalization to higher dimensions is obvious.) | |
| Feb 13, 2015 at 0:13 | comment | added | Włodzimierz Holsztyński | I think it goes back to the Witold Hurewicz's theorem. | |
| Feb 12, 2015 at 23:48 | comment | added | Douglas Zare | "It suggest that there are simply connected manifolds which are not homeomorphic to sphere." $S^2 \times S^2$ is a simple example. | |
| Feb 12, 2015 at 22:45 | comment | added | Qiaochu Yuan | In dimension $3$, a closed manifold which is simply connected is an integral homology sphere, and in all dimensions, a closed manifold which is simply connected and also an integral homology sphere is homotopy equivalent to a sphere. So the formulation is not so different. | |
| Feb 12, 2015 at 22:39 | history | asked | truebaran | CC BY-SA 3.0 |