Timeline for Is the top Stiefel-Whitney number of a topological manifold the Euler characteristic mod two?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 13, 2018 at 1:00 | vote | accept | Michael Albanese | ||
| Sep 10, 2018 at 20:27 | comment | added | mme | The proof of the classification is a reverse-induction on dimension; if there is some vector so that $B(x,x) = 1$, then split off $x$ as a summand. If not, pick an arbitrary nonzero vector $x_1$ and use nondegeneracy to find some vector $x_2$ with $B(x_1, x_2) = 1$. Split off this subspace as a summand (this uses nondegeneracy to see that the 'complement' is actually 2 dimensions less); the assumption that $B(x, x) = 0$ for all $x$ implies the bilinear form is given by the stated matrix on this summand. | |
| Sep 10, 2018 at 20:19 | history | undeleted | mme | ||
| Sep 10, 2018 at 20:19 | history | edited | mme | CC BY-SA 4.0 |
deleted 309 characters in body
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| Sep 10, 2018 at 19:55 | history | deleted | mme | via Vote | |
| Sep 10, 2018 at 19:45 | history | answered | mme | CC BY-SA 4.0 |