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Let $\gamma$ be the tautological line bundle over $\mathbb{CP}^1$. Is it possible to compute the second Stiefel Whitney Class $w_2(\gamma)$ from the axioms, and if so, can you give a hint how?

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  • $\begingroup$ You do not want to use the fact that the stiefel whitney classes are the mod 2 reductions of the chern classes? $\endgroup$ – Thomas Rot Nov 23 '16 at 15:17
  • $\begingroup$ @ThomasRot We haven't covered those yet (and we will), so I would rather do it without $\endgroup$ – Pepijn Nov 23 '16 at 19:24
  • $\begingroup$ One idea: There is a homotopically non-trivial map $RP^2\rightarrow S^2$, by mapping everything in the one skeleton to the southpole. Maybe one can understand what happens to the tautological bundle under this map. If this pullback has a non-zero $w_2$, one knows that the original bundle has a non-zero $w_2$. $\endgroup$ – Thomas Rot Nov 24 '16 at 15:35

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