Timeline for Jets in synthetic differential geometry
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 16, 2017 at 11:14 | comment | added | ಠ_ಠ | @DmitriZaitsev $R$ is the line object in some smooth topos, which plays the role of the real number line in SDG. | |
| Nov 16, 2017 at 11:09 | comment | added | Dmitri Zaitsev | What precisely is $R$ here? | |
| Jan 5, 2016 at 22:18 | history | edited | ಠ_ಠ |
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| Jan 5, 2016 at 21:49 | vote | accept | ಠ_ಠ | ||
| Dec 31, 2015 at 9:53 | answer | added | Michael Bächtold | timeline score: 8 | |
| Dec 31, 2015 at 0:39 | comment | added | ಠ_ಠ | I thought that $J^k(R^n, R^m)$ usually denotes the equivalence classes of maps $R^n \to R^m$ which agree up to their $k$th order Taylor expansion? | |
| Dec 30, 2015 at 20:11 | comment | added | Michael Bächtold | Upon further thought, your definition of $J^k(R^n,R^m)$ is not even the space of sections of non holonomic jets, but something more complicated, and your definition of $j^kf $ is also not what people usually mean by that. I'll write an answer if I have time. But Kock's book should contain an answer. | |
| Dec 30, 2015 at 14:23 | comment | added | Michael Bächtold | The definition you gave makes sense for arbitrary objects in a topos where $D_k(n)$ exists. Maybe it is not well behaved for your purposes? Also a small remark: the thing you defined as $J^k(R^n,R^m)$ is not what people usually denote with that symbol, but rather the space of (non-holonomic) sections of the space of jets. Also, have you seen the nice book by Anders Kock "Synthetic Geometry of Manifolds"? It also talks about jets in the synthetic context home.math.au.dk/kock/SGM-final.pdf | |
| Dec 30, 2015 at 13:42 | history | asked | ಠ_ಠ | CC BY-SA 3.0 |