Timeline for Second Stiefel Whitney class of quotients of odd spheres
Current License: CC BY-SA 3.0
4 events
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| Sep 16, 2013 at 10:21 | comment | added | José Figueroa-O'Farrill | @Italo: you will find that you will need to know something about $G$. For example, take $S^5$ and consider quotienting by a freely acting cyclic group contained in the circle group defining the fibration to $\mathbb{C}P^2$. Since $\mathbb{C}P^2$ is not spin, there is no guarantee that the resulting lens space is spin and you will find that depending on the order of the cyclic group it is not. On the other hand, for $S^7$, all freely-acting cyclic subgroups of $SO(8)$ and not just of $U(4)$ result in spin quotients. | |
| Sep 16, 2013 at 8:25 | vote | accept | Italo | ||
| Sep 16, 2013 at 8:24 | comment | added | Italo | Thank you very much! I want to calculate the second Stiefel Whitney class to determine if $X$ is spin!:) But about $G$ i know only that $G<U(n)$ and that acts freely on the sphere... I'll meditate on your construction! | |
| Sep 15, 2013 at 12:26 | history | answered | José Figueroa-O'Farrill | CC BY-SA 3.0 |