Timeline for Can you cover a genus a billion hyperbolic surface with 15 balls?
Current License: CC BY-SA 4.0
10 events
when toggle format | what | by | license | comment | |
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Jan 29, 2021 at 18:09 | answer | added | Will Sawin | timeline score: 4 | |
Jan 29, 2021 at 12:18 | vote | accept | biringer | ||
Jan 29, 2021 at 9:30 | answer | added | Moishe Kohan | timeline score: 13 | |
Jan 29, 2021 at 4:56 | comment | added | Moishe Kohan | Every nonorientable closed connected surface of negative Euler characteristic, admits a hyperbolic metric such that the surface is covered by 3 embedded disks. | |
Jan 29, 2021 at 2:57 | comment | added | biringer | I'm thinking open balls, although I doubt that matters, and yes, size the injectivity radius is allowed. (Pathwise isometrically embedded, i.e. Riemannianly embedded, not isometrically embedded.) But whatever, really. I initially thought this would be useful for something, but I'm not sure it is anymore. Thought it was curious enough to post though. | |
Jan 29, 2021 at 1:05 | comment | added | Ian Agol | Are your metric balls isometrically embedded in the surface? E.g., if I took a ball around a point of size the injectivity radius, would that be an embedded ball? And are the closed or open? | |
Jan 28, 2021 at 22:32 | history | edited | biringer | CC BY-SA 4.0 |
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Jan 28, 2021 at 20:41 | comment | added | biringer | Cool, good to know. 👍 | |
Jan 28, 2021 at 20:06 | comment | added | Will Sawin | The surfaces in Theorem 1.10 of the linked paper, which I think is what you are referencing, are Hurwitz surfaces, which are always compact. For example this is because they are finitely tiled by a particular bounded hyperbolic triangle. | |
Jan 28, 2021 at 19:29 | history | asked | biringer | CC BY-SA 4.0 |