Timeline for Four circles on the sphere
Current License: CC BY-SA 4.0
23 events
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| Oct 24, 2023 at 17:56 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Sep 29, 2018 at 22:01 | history | edited | j.c. | CC BY-SA 4.0 |
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| Sep 29, 2018 at 20:26 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Jun 13, 2018 at 19:28 | answer | added | Sam Benner | timeline score: 3 | |
| Jun 13, 2018 at 17:16 | comment | added | Alexandre Eremenko | @Wojowu: The reference for the asymptotics seems to be in the comment of მამუკა ჯიბლაძე. But our task was a complete list for n=4. | |
| Jun 13, 2018 at 14:39 | comment | added | Wojowu | One question I pondered the moment I saw the question is, how many configurations of $n$ circles are there? Can we give some asymptotic? Does anyone know a reference for that? | |
| Jun 13, 2018 at 14:07 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Jun 13, 2018 at 4:05 | comment | added | Paul Siegel | Speaking only for myself, there is no way I would have voted to close this question as trivial. | |
| Jun 13, 2018 at 3:32 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Jun 13, 2018 at 2:47 | comment | added | Gerry Myerson | If I'm reading the review of the Kang and Muller paper correctly, the five curve counterexample is due to J. Linhart and R. Ortner [Beiträge Algebra Geom. 46 (2005), no. 2, 351–356; MR2196921]. What Kang and Muller do is prove the Linhart-Ortner conjecture that this counterexample is minimal. | |
| Jun 13, 2018 at 2:02 | comment | added | Ryan Budney | Hi Alex, I asked a very similar question to yours, back in February. mathoverflow.net/questions/292671/… | |
| Jun 13, 2018 at 0:47 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Jun 12, 2018 at 16:20 | comment | added | Ivan Izmestiev | I suspect that your last edit (topological nature of the problem) is false. In the similar setting of arrangements of lines and pseudolines there exist so called nonstretchable arrangements of pseudolines. (Even if you require that at most two lines pass through each point.) An example with 9 lines can be "doubled" and an equator can be added so that one gets a "nonstretchable" arrangement of 10 Jordan curves on the sphere. | |
| Jun 12, 2018 at 14:40 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Jun 12, 2018 at 4:41 | comment | added | მამუკა ჯიბლაძე | Might be also related to the moduli space of quadratic differentials (see Figure 4 on page 7 in "Enumeration of meanders and Mazur-Veech volumes" by Delecroix, Goujard, Zograf and Zorich) | |
| Jun 12, 2018 at 0:34 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Jun 11, 2018 at 20:14 | comment | added | Ivan Izmestiev | Sphere arrangements (in the spirit of classical works on hyperplane arrangements) were studied in "Arrangements of spheres and projective spaces" by Deshpande, Rocky Mountain J. Math, 2016. | |
| Jun 11, 2018 at 20:10 | history | edited | j.c. | CC BY-SA 4.0 |
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| Jun 11, 2018 at 17:28 | comment | added | Igor Belegradek | The paper "Connected sum at infinity and Cantrell-Stallings hyperplane unknotting" by Jack S. Calcut, Henry C. King, and Laurent C. Siebenmann seems relevant, see 9.2, 9.3 in projecteuclid.org/euclid.rmjm/1361800607. | |
| Jun 11, 2018 at 17:19 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Jun 11, 2018 at 17:04 | history | edited | Alexandre Eremenko |
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| Jun 11, 2018 at 16:59 | history | edited | Neil Strickland | CC BY-SA 4.0 |
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| Jun 11, 2018 at 16:53 | history | asked | Alexandre Eremenko | CC BY-SA 4.0 |