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For questions about Stiefel-Whitney classes which are characteristic classes associated to real vector bundles.

13 votes

Is the top Stiefel-Whitney number of a topological manifold the Euler characteristic mod two?

It has been proved in the preprint (page 6) by Renee Hoekzema that the vanishing of the $w_{n}(M)$ implies $\chi(M)$ is even. The proof uses the fact that a symplectic vector space over $\mathbb{F}_{2 …
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