Timeline for "Thickening" an arc on a 2-manifold
Current License: CC BY-SA 4.0
6 events
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| Sep 9, 2022 at 11:29 | comment | added | Tim Campion | [Text continued from Palina Severyna's answer which was converted to a comment:] Finally, I've read the thread mathoverflow.net/questions/57766/… (you marked my question as duplicate to it) and couldn't understand in the argument of Bill Thurston, why the original arc can be identified with one of its two pre-images under the branched cover $z \to z^2$ of a sphere. What is a homeomorphism between them? I also would like to remark that I may not assume that the surface permits a triangulation. | |
| Sep 9, 2022 at 9:55 | comment | added | Palina Severyna | Unfortunately I don't have enough reputation to write a comment, so I have to use the answer field to ask for the clarification for the first proof idea here. @SamNead, could you please explain how one can apply the Jordan-Schoenflies to a surface? The statement of the theorem holds for now for a plane only. Then, it's also not so clear, why, for exmaple, a spiral arc $[0, 1] \to \mathbb{C}$, $t \mapsto (1 - t)e^{i \frac{1}{1 - t}}$, completed to a Jordan curve, has necesseraly an annulus neighbourhood. How exactly does it follow from the Jordan-Schoenflies? Finally, I've read the thread https | |
| Aug 30, 2022 at 1:25 | comment | added | Sam Nead | Yes, very relevant! Also, I notice that I, sometime in the past voted, up that post and some of the answers... We should probably mark this question (and my answer) as a duplicate. | |
| Aug 30, 2022 at 0:35 | comment | added | Jim Conant | Belevant: mathoverflow.net/questions/57766/… | |
| Aug 29, 2022 at 23:51 | history | edited | Sam Nead | CC BY-SA 4.0 |
added "two"
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| Aug 29, 2022 at 23:28 | history | answered | Sam Nead | CC BY-SA 4.0 |