Timeline for Example of bundle-mapping over $S^4$ with singularity $S^2$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 4, 2016 at 8:27 | vote | accept | DLIN | ||
| Jul 26, 2016 at 3:21 | answer | added | Shinichiro Nakamura | timeline score: 3 | |
| Jul 22, 2016 at 11:20 | comment | added | DLIN | For the point singularity case, there is an example. Since outside the equator $S^3$, $S^4\setminus S^3$ can shrink to points,we can use the standard identification, but near S3S3 we use the coordinate of the point by $(\alpha,\beta)\to\rho(\sqrt{|\alpha|^2+|\beta|^2})\left(\begin{array}{cc}\alpha&-\bar\beta\\ \beta&\bar\alpha \end{array}\right)$, where we use the complex coordinate $(\alpha,\beta)$ and $\rho$ is the cut off function near the point, by the partition of unity, we can have a global mapping. But I do not how to give the sphere singularity example. | |
| Jul 21, 2016 at 12:01 | history | asked | DLIN | CC BY-SA 3.0 |