Timeline for Recovering a smooth manifold from its tensor fields
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 21, 2016 at 16:03 | vote | accept | Alex M. | ||
| Jan 20, 2016 at 12:21 | comment | added | Alex M. | @user1504: No, I wasn't aware of Connes's theorem, your pointers to the other two questions are very helpful, thank you. They tell me that my question is intelligently posed, provided that I add some supplementary structure on $M$ (in Connes's case, a Riemannian structure). | |
| Jan 19, 2016 at 22:09 | comment | added | user1504 | That may be true, but one might as well know about Connes' theorem when asking this sort of question. Not totally clear from the 2nd paragraph if the OP did. | |
| Jan 19, 2016 at 21:59 | comment | added | Bertram Arnold | @user1504 To be pedantic: This gives you a condition for when an algebra is of the form $C^\infty(M)$ for some smooth manifold $M$ (which is difficult). If I understood the question right, it is about the next step, where we already know that the algebra in question is the algebra of functions of some manifold and try to reconstruct it algebraically. | |
| Jan 19, 2016 at 20:48 | comment | added | user1504 | What you want is Connes' reconstruction theorem. See Branimir Cacic's answers to mathoverflow.net/questions/16833/… and mathoverflow.net/questions/191720/commutative-spectral-triple | |
| Jan 19, 2016 at 19:24 | answer | added | Bertram Arnold | timeline score: 11 | |
| Jan 19, 2016 at 18:27 | history | asked | Alex M. | CC BY-SA 3.0 |