Timeline for Why is the integral of the second chern class an integer?
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4 events
| when toggle format | what | by | license | comment | |
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| Mar 29, 2011 at 15:44 | comment | added | Charlie Frohman | Or, as the poser of the question is familiar with "From Calculus to Cohomology" you can quote Theroem 18.4 on page 184. | |
| Mar 28, 2011 at 17:30 | comment | added | Donu Arapura | Let's say that you knew everything (functoriality, Whitney sum...) but the correct normalization. Then you'd have to calculate essentially one example: the universal bundle on a Grassmanian to get the correct constant. To do carry this out, pull it up to the flag manifold (you won't lose anything, since cohomology injects), split it has a sum of line bundles, and apply Whitney sum. That's what I meant in my previous comment. | |
| Mar 28, 2011 at 17:08 | comment | added | Greg Graviton | That is certainly true, but kind of dodges the question. One would have to show why the two agree up to a constant factor and then one would have to determine the constant factor to be precisely $(2\pi)^k$, and not, say $3\pi^{k/2}$. Both are currently beyond my understanding. | |
| Mar 28, 2011 at 16:56 | history | answered | Jessica L | CC BY-SA 2.5 |