Timeline for Cutting up the Bring surface into six pairs of pants
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| May 21, 2022 at 14:18 | comment | added | Lyle Ramshaw | @Gro-Tsen, my paper about viewing the polygon space of equilateral pentagons as the Bring sextic is now available on arXiv: link. See, in particular, pages 10 and 11. | |
| Feb 13, 2021 at 19:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 16, 2020 at 19:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 18, 2020 at 18:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| May 19, 2020 at 16:35 | answer | added | Lyle Ramshaw | timeline score: 2 | |
| May 15, 2020 at 17:19 | comment | added | Lyle Ramshaw | Rather than permuting the vertices of the equilateral pentagon, permute the order in which its edge vectors get assembled, tip to tail. The 24 $\frac{\pi}{5}$ vertices of the Bring sextic then correspond to the 24 pentagons whose five edges are evenly distributed around the unit circle, while the 30 $\frac{\pi}{4}$ vertices correspond to the 30 pentagons that have two pairs of coincident edges. | |
| May 15, 2020 at 14:05 | comment | added | Gro-Tsen | I am certainly curious to see this paper. But could you already explain what the automorphisms of order $2,4,5$ defining the triangle group $\Delta^0(2,4,5) \cong \mathfrak{S}_5$ acting on Bring's surface correspond to when acting on equilateral pentagons? (Or at least what are the fixed pentagon shapes under them?) Because the only action of $\mathfrak{S}_5$ on pentagons that I can think of is by permuting the vertices, and this doesn't preserve equilaterality, so I'm confused. | |
| May 15, 2020 at 3:33 | comment | added | Lyle Ramshaw | The polygon space for equilateral pentagons in the plane and the Bring sextic are both compact, orientable, smooth surfaces of genus 4, so there are lots of maps between them. I am drafting a 35-page paper about such a map, and I hope that people who are curious about this area will be interested in reading it. | |
| May 14, 2020 at 14:08 | comment | added | Gro-Tsen | Could you clarify your statement that “one can elegantly map all of the possible shapes of equilateral pentagons in the Euclidean plane to the points of the Bring sextic”? What is this map? (I just happened to be reading Matthias Weber's paper “Kepler's small stellated dodecahedron as a Riemann surface”, which is also about Bring's sextic, so I'm curious.) | |
| May 14, 2020 at 3:44 | history | edited | Lyle Ramshaw | CC BY-SA 4.0 |
Rewrite the formulas for the lengths of loops in the Bring sextic to show shared structure.
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| May 12, 2020 at 14:53 | history | edited | Lyle Ramshaw | CC BY-SA 4.0 |
Added $K_4$ as a simpler name for the edge-graph of a tetrahedron.
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| May 12, 2020 at 3:23 | history | asked | Lyle Ramshaw | CC BY-SA 4.0 |