Timeline for References on principal G bundle and connections
Current License: CC BY-SA 4.0
28 events
| when toggle format | what | by | license | comment | |
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| S Jul 12, 2023 at 15:10 | history | suggested | ARA | CC BY-SA 4.0 |
fixed grammar
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| Jul 12, 2023 at 14:28 | review | Suggested edits | |||
| S Jul 12, 2023 at 15:10 | |||||
| May 31, 2020 at 7:59 | answer | added | Ben McKay | timeline score: 3 | |
| May 31, 2020 at 7:03 | answer | added | Praphulla Koushik | timeline score: 2 | |
| Dec 16, 2017 at 16:51 | comment | added | Praphulla Koushik | @nfdc23 I was not particular about page number... I will have a Lok at those two chapters. Thanks | |
| Dec 16, 2017 at 15:35 | comment | added | nfdc23 | By the way, the published edition of Spivak's Volume II to which I referred (for the page number of (*), for example) is the LaTeX version, not the original published version (which probably had different page numbers). | |
| Dec 16, 2017 at 9:53 | answer | added | Mozibur Ullah | timeline score: 4 | |
| Dec 16, 2017 at 6:16 | comment | added | Praphulla Koushik | I have not read that. I will read that and will come back if I have any further questions @nfdc23 | |
| Dec 16, 2017 at 5:43 | comment | added | nfdc23 | Have you tried reading Chapter 8 of Volume II of Spivak's tomes on differential geometry (where (*) mentioned early on refers to an equation at the bottom of page 280 in Chapter 7)? It is somewhat formula-intensive, but does carefully address the passage between principal Ehresmann connections on principal bundles and the more classical Koszul connection viewpoint on rank-$n$ vector bundles, and has a nice Summary at the end of the chapter for passing among various viewpoints on connections. The end of the Wikipedia article on connections that @DeaneYang mentions ties up related loose ends. | |
| Dec 16, 2017 at 5:20 | history | edited | Praphulla Koushik | CC BY-SA 3.0 |
added 276 characters in body; edited tags
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| S Dec 3, 2017 at 17:29 | history | bounty ended | CommunityBot | ||
| S Dec 3, 2017 at 17:29 | history | notice removed | CommunityBot | ||
| Nov 26, 2017 at 18:11 | comment | added | Deane Yang | The wikipedia article en.wikipedia.org/wiki/Connection_form#Principal_bundles looks like a reasonable explanation of all this. | |
| Nov 26, 2017 at 18:11 | comment | added | Deane Yang | I find the moving frame approach using differential forms the easiest, because the Maurer-Cartan equations are easiest to use in that form. Also, it's easier to view $G$ as a subgroup of $GL(n)$ (the fancy way to say that is the fiber of the vector bundle is a faithful representation of $G$ but you don't need to know that at first). | |
| Nov 26, 2017 at 18:01 | comment | added | Deane Yang | Unfortunately, I'm terrible with references. I usually learn bits and pieces from different sources and then try to put it all together in a consistent framework (of which choosing a consistent notation that I like is important). The problem is that there are three distinct ways to approach anything: local coordinates, vector fields, and differential forms ("moving frames"). | |
| Nov 26, 2017 at 13:47 | comment | added | Praphulla Koushik | @DeaneYang thanks for your comment. Can you give some reference where you have seen about bundl elf frames on a vector bundle. | |
| Nov 26, 2017 at 1:05 | comment | added | Deane Yang | I don't know if this is helpful or not, but I find it easier to figure out what a connection on a principal bundle is, if I view the principal bundle as a bundle of frames on a vector bundle and the connection on the principal bundle as a connection on the vector bundle acting on a "moving frame". That helps make the definition of a connection in, say, Kobayashi-Nomizu easier to understand. | |
| Nov 26, 2017 at 0:24 | answer | added | Craig | timeline score: 5 | |
| S Nov 25, 2017 at 16:26 | history | bounty started | Praphulla Koushik | ||
| S Nov 25, 2017 at 16:26 | history | notice added | Praphulla Koushik | Authoritative reference needed | |
| Nov 18, 2017 at 1:13 | comment | added | Praphulla Koushik | @WilleLiou thanks for the comment. Can you suggest some place where I can find most of these definitions discussed. | |
| Nov 18, 2017 at 1:12 | comment | added | Praphulla Koushik | @PiotrAchinger : I will see that notes. Thank you. | |
| Nov 18, 2017 at 1:09 | comment | added | Praphulla Koushik | @abx I will understand that they are equivalent as you said it is needed to understand what a connection is, Can you give some reference where most of these equivalent definitions arey mentioned. | |
| Nov 17, 2017 at 21:44 | comment | added | Wille Liu | @abx, I don't see why 'they' are all obviously equivalent, at least not for the one given by op and the one given by local trivialisation and gluing. | |
| Nov 17, 2017 at 21:17 | comment | added | Piotr Achinger | I liked José Figueroa-O'Farrill's notes on gauge theory. You might find the first two lectures enlightening: empg.maths.ed.ac.uk/Activities/GT | |
| Nov 17, 2017 at 19:43 | comment | added | abx | "Some other definition": all these definitions are easily seen to be equivalent. | |
| Nov 17, 2017 at 17:26 | review | First posts | |||
| Nov 17, 2017 at 17:35 | |||||
| Nov 17, 2017 at 17:23 | history | asked | Praphulla Koushik | CC BY-SA 3.0 |