Timeline for $S^n \to S^m \to B$ bundle: possible?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 3, 2010 at 2:54 | comment | added | David Roberts♦ | that should be $R^{10}$ not $R^10$. $C^*$ is the nonzero complex numbers. | |
| Nov 3, 2010 at 2:54 | comment | added | David Roberts♦ | $CP^4 = (C^5-0)/C^*$, and since $C^5 \simeq R^10$, we can get an isomorphism $(C^5-0)/C^* \simeq S^9/U(1)$. So take $S^9 \subset C^5$ and then quotient by the natural diagonal action of the complex numbers of unit length. | |
| Nov 3, 2010 at 2:37 | comment | added | Romeo | @Spiro: thanks for adding the other 2 classics! | |
| Nov 3, 2010 at 2:36 | comment | added | Romeo | What's the map $S^9 \to CP^4$ giving a circle bundle? | |
| Nov 3, 2010 at 2:33 | comment | added | José Figueroa-O'Farrill | These are certainly the only examples where all three spaces are spheres. But certainly there are more: all complex projective spaces have circle bundles whose total spaces are spheres. | |
| Nov 3, 2010 at 2:25 | history | answered | Spiro Karigiannis | CC BY-SA 2.5 |