Timeline for Sheaves and bundles in differential geometry
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| S Dec 24, 2022 at 15:20 | history | suggested | user234212323 |
added a tag
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| Dec 24, 2022 at 0:41 | review | Suggested edits | |||
| S Dec 24, 2022 at 15:20 | |||||
| Jun 5, 2014 at 8:40 | comment | added | Lennart Meier | In a different vein: While only few people would define a manifold as a locally ringed space such that ..., this viewpoint is quite common if one treats supermanifolds. | |
| Jun 5, 2014 at 8:36 | comment | added | Lennart Meier | More part of differential topology than of differential geometry, but Gromov made good use of (microflexible) sheaves with his h-principle about partial differential relations, giving you theorems about immersions, submersion etc. | |
| May 22, 2010 at 3:59 | answer | added | Konrad Waldorf | timeline score: 4 | |
| Mar 9, 2010 at 5:01 | answer | added | Deane Yang | timeline score: 32 | |
| Mar 9, 2010 at 3:35 | vote | accept | Harry Gindi | ||
| Mar 9, 2010 at 3:29 | answer | added | Emerton | timeline score: 120 | |
| Mar 9, 2010 at 2:46 | comment | added | Harry Gindi | Sure, but my point was more about the overwhelming prominence of bundles in DG, while sheaves get relatively little exposure in that setting. Bundles are used much more often in AG than sheaves are used in DG, at least in my experience. | |
| Mar 9, 2010 at 2:22 | comment | added | Ilya Grigoriev | There is the obvious answer: a lot in mathematics depends on your point of view. Sometimes you care more about spaces themselves, and sometimes you care more about the functions/sections on the spaces. It seems to me to be counterproductive to force yourself to translate everything to the same language, regardless of what the problem you're dealing with is best suited to. That said, I'd be quite interested in what other people have to say about less subjective advantages. | |
| Mar 9, 2010 at 0:10 | comment | added | Harry Gindi | I must note that by "any bundle constructions that don't have a realization as a sheaf", I mean any useful bundle constructions that don't have a realization as a sheaf. I am aware of the adjunction between $Psh(X)$ and $Bundle(X)$, which restricts to an equivalence of categories on $Sh(X)$ and some subcategory of $Bundle(X)$ that I don't remember offhand (they are covering spaces in the continuous case.) | |
| Mar 8, 2010 at 23:07 | history | asked | Harry Gindi | CC BY-SA 2.5 |