Timeline for How to prove that $w_1(E)=w_1(\det E)$?
Current License: CC BY-SA 4.0
11 events
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| Oct 10, 2018 at 23:26 | comment | added | Dan Ramras | @AlexM. I've updated the link (when I went to edit the post, it seemed the word "notes" was supposed to be a link, but for some reason it hadn't looked like it in the original post). The full notes are here: math.iupui.edu/~dramras/697.html | |
| Oct 10, 2018 at 23:22 | history | edited | Dan Ramras | CC BY-SA 4.0 |
corrected link
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| Oct 5, 2018 at 8:49 | comment | added | Alex M. | @DanRamras: "This is spelled out in my notes on vector bundles" - could you please give us a link to them? Thank you. | |
| S Jul 3, 2018 at 5:52 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
en latexified
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| S Jul 3, 2018 at 5:52 | history | suggested | janmarqz | CC BY-SA 4.0 |
en latexified
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| Jul 3, 2018 at 1:22 | review | Suggested edits | |||
| S Jul 3, 2018 at 5:52 | |||||
| Apr 17, 2010 at 13:04 | history | edited | Ben Webster♦ | CC BY-SA 2.5 |
added 8 characters in body
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| Apr 17, 2010 at 12:16 | comment | added | Dan Ramras |
Bundles over the circle are pretty simple things... They're classified by maps into the Grassmanian, so you need to think about the fundamental group of the Grassmanian. This is just $Z/2 =\pi_1 BO(n)= \pi_0 O(n)$, so there are only two of them in each dimension. This is also discussed in my notes :)
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| Apr 17, 2010 at 12:09 | history | edited | Dan Ramras | CC BY-SA 2.5 |
correctly corrected typo
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| Apr 17, 2010 at 12:08 | comment | added | Qfwfq | For vector bundles, shouldn't the question answered by $w_1(E)$ be something like "along which loops is $E$ orientable?". For line bundles over the circle orientability is the same as nontriviality, but for higher rank bundles? (b.t.w. I havent read all the answer carefully yet: I will do it later!) | |
| Apr 17, 2010 at 11:59 | history | answered | Dan Ramras | CC BY-SA 2.5 |