Timeline for Sheaf-theoretically characterize a Riemannian structure?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 3, 2018 at 23:03 | comment | added | Qfwfq | @bianchira: as for me, sure :) | |
| Jun 3, 2018 at 17:50 | history | edited | zzz | CC BY-SA 4.0 |
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| Jun 3, 2018 at 17:42 | comment | added | zzz | @Qfwfq indeed sorry did not see that question, but as there’s some good discussion in this thread now maybe we keep this open rather than closing it as duplicate? | |
| Jun 3, 2018 at 13:36 | comment | added | Qfwfq | This is very similar to (maybe almost a duplicate of) this question: mathoverflow.net/questions/56833/… | |
| Jun 3, 2018 at 11:15 | answer | added | Liviu Nicolaescu | timeline score: 16 | |
| Jun 3, 2018 at 6:47 | comment | added | Will Sawin | Lipschitz functions do not form an algebra. Maybe one in fact needs also the map from the sheaf of Lipschitz functions to the sheaf of continuous functions. Using maximal ideals in the sheaf of continuous functions, one can define the evaluation map. Then one simply defines the distance between two points as the maximum difference between their evaluations in any connected open set containing both points. | |
| Jun 3, 2018 at 6:38 | comment | added | zzz | @WillSawin thanks! my analysis is rusty - is there a textbook reference for how the algebra of lipschitz functions lets you recover the metric? | |
| Jun 3, 2018 at 6:12 | history | edited | zzz | CC BY-SA 4.0 |
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| Jun 3, 2018 at 5:59 | comment | added | Will Sawin | I think the sheaf of locally Lipschitz functions with Lipschitz constant $1$ will do the trick, as it will tell you the metric (in the metric spaces sense), which determines the metric (in the Riemmanian metric sense). | |
| Jun 3, 2018 at 5:46 | history | asked | zzz | CC BY-SA 4.0 |