Timeline for Composition of bibundles
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 30, 2023 at 8:18 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
Fixed small error
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| Nov 27, 2023 at 5:46 | comment | added | David Roberts♦ | @Connor thanks! I should fix it. | |
| Nov 27, 2023 at 4:06 | comment | added | Connor Grady | I just wanted to point out a small error in the second paragraph in case anyone else gets confused like I did. Namely that $\mathbf{B}G$ should not act trivially on $u(H)$, it should act via $\phi$. This is implicit in the next paragraph though, so no harm, no foul :) | |
| Sep 27, 2018 at 7:56 | comment | added | Praphulla Koushik | You said "No, you don't think about the H-bundle $P\times H\rightarrow P$, all bundles you are considering should be over M. Why not ask another question..." Yes.. I was thinking something else.. I understand that and added that in my answer. Thanks.. | |
| Sep 26, 2018 at 10:46 | comment | added | Praphulla Koushik | Let us continue this discussion in chat. | |
| Sep 26, 2018 at 6:41 | comment | added | Praphulla Koushik | I do not know how to read your comment as :P I understand the point more clearly after rewriting your answer... Thanks :D | |
| Sep 26, 2018 at 6:38 | comment | added | David Roberts♦ | You have indeed faithfully rewritten my answer using different notation :-) | |
| Sep 26, 2018 at 6:18 | comment | added | Praphulla Koushik | Thanks. I will see that. Do you think I got the rough idea correctly atleast? | |
| Sep 26, 2018 at 6:13 | comment | added | David Roberts♦ | en.wikipedia.org/wiki/Associated_bundle gives a hint, but if you can access it, this is definitive: doi.org/10.1007/978-1-4757-2261-1_6. Or see Definition 5.5 in the sequel, mathematik.uni-muenchen.de/~schotten/Texte/… | |
| Sep 26, 2018 at 6:01 | comment | added | Praphulla Koushik | I have written in my words what you said. Let me know if I have missed anything. I am not very comfortable with changing the structure group along a morphism of Lie groups. If you can suggest some reference for the same it will be helpful. | |
| Sep 26, 2018 at 4:13 | comment | added | Praphulla Koushik | Ok.. I am also trying to rewrite your answer in my own words and in my own notation so that I can appreciate it more than what I do now.. I do not mean I am editing your answer... Your explanation is super clear and I have no doubt about that... | |
| Sep 26, 2018 at 4:09 | comment | added | David Roberts♦ | I'm not sure what else I would say. I prefer my counterexample to your counterexample, as it is shorter and less confusing to me. | |
| Sep 26, 2018 at 2:40 | comment | added | Praphulla Koushik | Can you check my other replies to this question as answers. YOur comments would be helpful.. | |
| Sep 11, 2018 at 3:35 | vote | accept | Praphulla Koushik | ||
| Jul 15, 2018 at 12:46 | comment | added | David Roberts♦ | The notation $\mathbf{B}G$ means the Lie groupoid whose object manifold is $\{pt\}$ and whose arrow manifold is denoted $G$. It follows from the axioms that $G$ is nothing else than a Lie group. If I were to write the stack of $G$-bundles, which is the stackification of this Lie groupoid, I would write it as $\mathrm{Bun}_G$ or similar. | |
| Jul 6, 2018 at 20:17 | comment | added | Praphulla Koushik | I am having little difficulty with the notations.. When you say “BG is one-object Lie groupoid” you mean $G$ is a Lie group, we have a groupoid associated to a Lie group, object set is Singleton, morphism set is G, usually written as $\{G\rightrightarrows *\}$.. you are calling this associated Lie groupoid also by G and then you are considering stack associated to Lie groupoid G(in your notation) and calling it BG. Is this correct? Or are you calling Lie groupoid it self by $BG$? | |
| Jul 4, 2018 at 12:23 | comment | added | Praphulla Koushik | Hello, I am with so much pending work :( I will respond in 2/3 days. Apologies. Thanks for your answer. I am sure it will make a difference :) | |
| Jul 4, 2018 at 3:33 | history | answered | David Roberts♦ | CC BY-SA 4.0 |