Timeline for Intuition/idea behind a proof of the splitting principle?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 4, 2016 at 23:55 | vote | accept | Student | ||
| Feb 5, 2016 at 0:02 | comment | added | Denis Nardin | @DanielLitt I don't think it explains it. I know the proof but in the end it boils down to a special property of the cohomology of projective space (that it is a power series ring in one variable) plus the Leray-Hirsch theorem. I find this quite mysterious in fact but I'd welcome a good intuition | |
| Feb 4, 2016 at 22:31 | comment | added | Daniel Litt | Well, in the flag formulation, $F(E)$ is an iterated projective bundle, which explains the injectivity on cohomology... | |
| Feb 4, 2016 at 22:17 | comment | added | David E Speyer | Good point. I don't have an immediate intuition for that but I'll think about it | |
| Feb 4, 2016 at 22:15 | comment | added | Denis Nardin | I guess that the miracle here is less that there is an universal splitting (as you say it is quite trivial) and more that the map in K-theory (and integral cohomology) is injective. | |
| Feb 4, 2016 at 22:02 | history | answered | David E Speyer | CC BY-SA 3.0 |