Timeline for Synthetic vs. classical differential geometry
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 18, 2016 at 7:54 | comment | added | Trent | I have a variant of this question which is too similar to warrant making a seperate thread for: what are some things in regular differential geometry that are crucial to understand if one wishes to understand differential geoemtry and which haven't (yet) been reformulated in sdg? | |
| Jan 5, 2016 at 22:17 | history | edited | ಠ_ಠ |
edited tags
|
|
| May 19, 2015 at 2:04 | comment | added | ಠ_ಠ | I am interested in differential geometry, and as far I know there is no theory of differential geometry formulated in terms of hyperreals. The synthetic approach also appears to be much more powerful: the setting for the theory is a topos, and the tangent bundle is representable. | |
| May 19, 2015 at 1:44 | comment | added | Christopher King | If you like infinitesimals, look up hyperreals. They're the best in terms of calculus. | |
| May 8, 2015 at 6:09 | history | edited | ಠ_ಠ | CC BY-SA 3.0 |
added 35 characters in body
|
| Nov 16, 2014 at 22:03 | answer | added | k g | timeline score: 6 | |
| Nov 16, 2014 at 16:13 | answer | added | user44143 | timeline score: 5 | |
| Nov 16, 2014 at 13:59 | answer | added | Thomas Holder | timeline score: 6 | |
| Nov 13, 2014 at 11:52 | vote | accept | ಠ_ಠ | ||
| Nov 12, 2014 at 0:37 | comment | added | user40276 | It's just a generalization of $C^{\infty}$-rings and the Weil functors. The relation to stacks is not very clear to me. However a fiber of a differentiable map is not a differentiable stack (in a natural way at least), while in the case of $C^{\infty}$-rings, it's a $C^{\infty}$-ring. | |
| Nov 12, 2014 at 0:04 | answer | added | Urs Schreiber | timeline score: 46 | |
| Nov 11, 2014 at 22:36 | comment | added | Steve Huntsman | As someone who doesn't actually know any SDG, it seems like one of SDG's most attractive practical aspects could/would be for proving theorems in an interactive proof assistant (at least this notion was why I bought an as-yet unread book on the topic). | |
| Nov 11, 2014 at 21:07 | comment | added | Andy Putman | I think that most mainstream work in Riemannian geometry ignores SDG. Though I'm only on the boundary of Riemannian geometry, my impression is that there really isn't a "foundational crisis". The biggest issues are related to things where category theory is mostly pretty useless, like analysis. | |
| Nov 11, 2014 at 20:40 | answer | added | Spinorbundle | timeline score: 7 | |
| Nov 11, 2014 at 20:34 | comment | added | Dan Petersen | There's an interesting recent book by Paugam that you might like (although I've only looked briefly at a few chapters), "Towards the Mathematics of Quantum Field Theory". The goal of his book is to formulate QFT mathematically in the most "correct" way possible, which for him means in terms of SDG, diffeological spaces, and homotopical algebra. | |
| Nov 11, 2014 at 19:47 | answer | added | David Carchedi | timeline score: 14 | |
| Nov 11, 2014 at 18:19 | history | asked | ಠ_ಠ | CC BY-SA 3.0 |