Timeline for manifold with given rational homology
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 29, 2011 at 5:32 | vote | accept | Markus Ulke | ||
| Jul 28, 2011 at 21:21 | answer | added | Lennart Meier | timeline score: 5 | |
| Jul 28, 2011 at 15:48 | answer | added | Mark Grant | timeline score: 7 | |
| Jul 28, 2011 at 0:06 | answer | added | Igor Rivin | timeline score: 3 | |
| Jul 27, 2011 at 22:42 | comment | added | Ryan Budney | Oh. I didn't understand what you meant by "where it is Q". You're saying in dimensions $0, 8$ and $16$ the homology has to have rank $1$. | |
| Jul 27, 2011 at 21:46 | answer | added | Neil Strickland | timeline score: 13 | |
| Jul 27, 2011 at 21:44 | comment | added | Greg Friedman | I'd say start with CP^8 and do surgery. Unfortunately, that's not very explicit, but I think you can argue this way that it exists. Alternatively, you might be able to do it with a plumbing construction. I'd recommend starting with Browder's book on surgery theory. | |
| Jul 27, 2011 at 21:43 | comment | added | Markus Ulke | the intend is to find something similar like cayleys projective plane in dimension 16 (at least rational). Up to now nobody i knew did find such a thing, the general opinion is that it does probably exist. (With Z replaced by Q it cant exist, but allowing torsion might render it possible) | |
| Jul 27, 2011 at 21:39 | comment | added | Markus Ulke | no the product above has homology $Q^2$ in dimension 8 hasnt it. Homology $Q^1$ is requested. | |
| Jul 27, 2011 at 21:17 | comment | added | Ryan Budney | There are simpler examples if you allow boundary. IMO a question like this is more appropriate for math.stackexchange.com. | |
| Jul 27, 2011 at 21:15 | comment | added | Ryan Budney | $S^8 \times S^8$ works. | |
| Jul 27, 2011 at 21:03 | history | asked | Markus Ulke | CC BY-SA 3.0 |