Timeline for Why do we use the less simple convention for the definition of a vector bundle connection?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 1, 2013 at 5:31 | answer | added | Grimolatto | timeline score: 1 | |
| Feb 8, 2013 at 0:32 | comment | added | S. Carnahan♦ | I am inclined to disagree with your claim that begins with "one normally defines". It is a convention that depends on the author, and varies across the literature. | |
| Feb 7, 2013 at 21:39 | comment | added | Amin | Oups sorry I just looked at A. Stacey's comment; sorry if this is what it was saying... | |
| Feb 7, 2013 at 21:37 | comment | added | Amin | The way I survived, heuristically, so far, is as follows. Notice that the factors in the tensor products are permuted in the two approaches. If from the second approach, you want to get to the first, you have to "pass" the $\omega$ (on the right) above the $\nabla(v)$ (which is on the left in the 2nd approach). This second factor is a bundle valuated one form, ie locally a one form tensor a section of $V$, hence you reobtain the $(-1)^k$. It's a bit sketchy but I've been ok with it. | |
| Feb 7, 2013 at 18:18 | comment | added | Andrew Stacey | Probably because people often skip parentheses, whereupon $\nabla \nu \wedge \omega$ is ambiguous as opposed to $\omega \wedge \nabla \nu$ which is not. | |
| Feb 7, 2013 at 17:30 | history | asked | Mihail Matrix | CC BY-SA 3.0 |