Timeline for How to show that a space has the homotopy type of wedge of spheres ?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 27, 2010 at 18:32 | vote | accept | Priyavrat Deshpande | ||
| Oct 27, 2010 at 3:18 | comment | added | Ryan Budney | If you can't get your hands on $\pi_1$ I doubt there's much likelyhood you'll be able to prove this space is a wedge of spheres -- which is a much harder problem. | |
| Oct 27, 2010 at 0:58 | comment | added | Priyavrat Deshpande | I can express $\pi_1$ as a colimit of fundamental groups of the spaces in a diagram, other than that I don't know anything in general. In case of the examples I could do by hand, I Was able to directly observe the wedge product hence I didn't bother to calculate the colimit and verify at the level of $\pi_1$. | |
| Oct 26, 2010 at 22:56 | comment | added | Ryan Budney | Of course it helps. If $\pi_1 X$ isn't a free group you know for certain $X$ doesn't have the homotopy-type of a wedge of spheres. Do you have anything to indicate $\pi_1 X$ is trivial? | |
| Oct 26, 2010 at 22:26 | comment | added | Priyavrat Deshpande | Computation of $\pi_1$ doesn't really help because in higher dimensions $S^1$ is absent. | |
| Oct 26, 2010 at 21:42 | answer | added | Dan Ramras | timeline score: 4 | |
| Oct 26, 2010 at 20:44 | answer | added | Paolo Aceto | timeline score: 3 | |
| Oct 26, 2010 at 20:30 | answer | added | Mikael Vejdemo-Johansson | timeline score: 4 | |
| Oct 26, 2010 at 19:15 | comment | added | Ryan Budney | Your situation is pretty generic, so unless you have some further input data there's not a whole lot to say. Can you compute $\pi_1 X$ and show it's free? That would be a start. | |
| Oct 26, 2010 at 18:40 | history | asked | Priyavrat Deshpande | CC BY-SA 2.5 |