Timeline for (Geometric) Proof for the projective bundle formula in K-theory
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 15, 2016 at 12:58 | vote | accept | Saal Hardali | ||
| Apr 15, 2016 at 9:44 | answer | added | Neil Strickland | timeline score: 6 | |
| Apr 14, 2016 at 23:16 | comment | added | Saal Hardali | @MarkHoyois sorry but although i see now why there should be a map like you suggest I fail to see how to define the kozul complex over $P(E)$ explicitly | |
| Apr 14, 2016 at 23:05 | comment | added | Marc Hoyois | @SaalHardali $H$ is the dual of the tautological bundle. The tautological bundle is tautologically a subbundle of the pullback of $E$ to $\mathbb P(E)$. It seems to me that $\lambda_E$ being a generator is equivalent to Bott periodicity, by the way. | |
| Apr 14, 2016 at 22:59 | comment | added | Saal Hardali | @MarcHoyois what does this map do over a point $l_x \in P(E)$? (Line in $E_x$) | |
| Apr 14, 2016 at 22:51 | comment | added | Marc Hoyois | Over $\mathbb P(E)$ your Koszul complex starts with $\mathbb C\hookrightarrow E\otimes H$, that's why you have powers of $[H]$. | |
| Apr 14, 2016 at 22:20 | comment | added | Denis Nardin | I think it is likely, although I cannot see all the details (btw for point 2 you might want to use the long exact sequence in K-theory from the cofiber sequence together with the surjectivity of some map). Also the best way to prove the Thom isomorphism is, in my opinion, the proof in Milnor-Stasheff. It's simple short and easy to remember | |
| Apr 14, 2016 at 22:14 | history | edited | Saal Hardali | CC BY-SA 3.0 |
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| Apr 14, 2016 at 22:14 | comment | added | Saal Hardali | @DenisNardin Thanks for the suggestion. Do you think the kind of proof i'm aiming at is possible? | |
| Apr 14, 2016 at 22:12 | comment | added | Denis Nardin | I know it is not the proof you're trying to get, but the usual proof uses the Atiyah-Hirzebruch-Serre spectral sequence for K-theory (or, if you prefer, the Leray-Hirsch theorem) | |
| Apr 14, 2016 at 22:03 | history | edited | Saal Hardali | CC BY-SA 3.0 |
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| Apr 14, 2016 at 21:47 | history | edited | Saal Hardali | CC BY-SA 3.0 |
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| Apr 14, 2016 at 21:38 | history | asked | Saal Hardali | CC BY-SA 3.0 |