Timeline for Quotienting disk inside sphere result in sphere
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 1, 2014 at 0:58 | comment | added | HJRW | You might try looking at Kwun, Kyung Whan, 'Upper semicontinuous decompositions of the n-sphere' Proc. Amer. Math. Soc. 13 1962 284–290. | |
| Jul 31, 2014 at 5:20 | comment | added | Ilias A. | user39082. If I remember, you can find this result in Hirschhorn book about localizations for example ... | |
| Jul 30, 2014 at 13:06 | comment | added | ThiKu | Well, then where is it proved that topological spaces form a left proper model category? Somewhere one has to prove something topologically, it can not all just be a game of defining and reformulating :-) | |
| Jul 29, 2014 at 17:41 | comment | added | Ilias A. | Push-out of a weak equivalence along a cofibration is a weak equivalence in a left proper model category (you can take it as a definition of left properness). | |
| Jul 29, 2014 at 16:11 | comment | added | ThiKu | So where is it proved that pushouts of weak equivalences are weak equivalences? | |
| Jul 28, 2014 at 22:57 | comment | added | Ilias A. | Since the category of topological space is left proper, the map $f:S^{k}\rightarrow W$ is a weak equivalence. If $W$ is a manifold then by generalized poincare (conjecture, now a theorem) $W$ is homeomorphic to $S^{k}$. So you need to find under which condition on $q$, $W$ is a manifold (actually compact). | |
| Jul 28, 2014 at 22:47 | comment | added | Prasit | @Fedotov If you don't mind, can you please expand on the idea? I did not follow the conclusion part. | |
| Jul 28, 2014 at 22:09 | comment | added | Ilias A. | Your question is equivalent to the following one: for which q, W is a k-manifold, and then you conclude by left properness and rigidity of the k-spheres. | |
| Jul 28, 2014 at 18:06 | history | edited | Prasit | CC BY-SA 3.0 |
added 187 characters in body
|
| Jul 28, 2014 at 15:21 | history | asked | Prasit | CC BY-SA 3.0 |