Timeline for Second Stiefel Whitney class of quotients of odd spheres
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Jul 3, 2018 at 15:54 | comment | added | Danny Ruberman | I don't know where this is written, but it is exactly the same as the argument for real projective spaces. For $m$ odd, the mod $2$ cohomology is trivial (except in the top dimension) so the Stiefel-Whitney classes vanish. ($w_{2n-1} = $ mod 2 Euler class $=0$ for dimension reasons.) For $m$ even, the mod 2 cohomology is the same as the cohomology of projective space. The tangent bundle is stably a power of the bundle $\lambda$, and so the answer is exactly the same as for the projective space of the same dimension. | |
| Jul 2, 2018 at 0:03 | comment | added | Michael Albanese | Do you know if the argument for lens spaces is written up anywhere? | |
| Sep 15, 2013 at 20:20 | history | answered | Danny Ruberman | CC BY-SA 3.0 |