Timeline for Small examples of exceptional hyperbolic Dehn Filling of hyperbolic manifolds
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 1, 2022 at 8:34 | comment | added | Sam Nead | More messing about with SnapPy suggests that L8a2 (katlas.org/wiki/L8a2) works. This makes sense, as it is a fairly nice filling of your example. I'll draw a picture and add this as another answer. | |
| Jul 1, 2022 at 8:06 | comment | added | Sam Nead | Or: we could look at the two-component links, having the figure-eight as one component, and hope to spot this example among those... A symmetry argument could prove that the core of the other component self intersects? | |
| Jul 1, 2022 at 8:04 | comment | added | Sam Nead | Ok, I played around a bit with Matthias's new version of "inside view" in snappy. It seems that there are two shortest immersed geodesics in the figure eight-knot complement. They have complex length $2.63391579384963 + 3.14159265358979i$ and, in unsimplified generators, they are represented by the words $abaB$ and $bbCC$. Instead of living in the immersed geodesic surface, they run from edge midpoint to edge midpoint inside the tetrahedra. So staring at the tetrahedra, as mapped into the diagram, might let us draw the desired diagram. | |
| Jul 1, 2022 at 6:16 | history | answered | Ian Agol | CC BY-SA 4.0 |