Timeline for How to prove that $w_1(E)=w_1(\det E)$?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 11, 2018 at 0:07 | comment | added | Tobias Shin | You can prove the identity for line bundles by proving it for the universal bundles over RP^inf, which follows from the Kunneth isomorphism. | |
| S Jul 3, 2018 at 4:49 | history | edited | Ivan Izmestiev | CC BY-SA 4.0 |
en latexified
|
| S Jul 3, 2018 at 4:49 | history | suggested | janmarqz | CC BY-SA 4.0 |
en latexified
|
| Jul 3, 2018 at 1:24 | review | Suggested edits | |||
| S Jul 3, 2018 at 4:49 | |||||
| Apr 17, 2010 at 11:59 | answer | added | Dan Ramras | timeline score: 11 | |
| Apr 17, 2010 at 9:50 | vote | accept | Qfwfq | ||
| Apr 17, 2010 at 9:50 | |||||
| Apr 17, 2010 at 9:50 | vote | accept | Qfwfq | ||
| Apr 17, 2010 at 9:50 | |||||
| Apr 17, 2010 at 9:36 | answer | added | Thorny | timeline score: 12 | |
| Apr 17, 2010 at 9:19 | comment | added | Qfwfq | Ok, Allen Hatcher proves that $w_1(L\otimes L')=w_1(L)+w_1(L')$ for line bundles. But he uses a "Leray-Hirsch" definition of characteristic classes, not the axiomatic one. Also, the proof that $w_1(L\otimes L')=w_1(L)+w_1(L')$ uses the property of the classifying space -not just the axioms- and is relatively complicated. I would've thought there was a one-line-proof directly from the axioms... | |
| Apr 17, 2010 at 8:55 | comment | added | Qfwfq | @Martin: doing so, it's my impression that one is led to compare $w1(L1)+ \cdots + w1(Ln)$ with $w1(L1 \otimes \cdots \otimes Ln)$. How does $w1$ behave with respect to tensor products of line bundles? | |
| Apr 17, 2010 at 7:13 | comment | added | Martin Brandenburg | splitting principle, reduce to line bundles. | |
| Apr 17, 2010 at 6:56 | history | asked | Qfwfq | CC BY-SA 2.5 |