Timeline for What is the complex structure on the boundary torus of a hyperbolic knot complement?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 1, 2014 at 22:36 | comment | added | Sam Nead | @Ryan - According to SnapPy, the knot K5_15 in the census CensusKnots has merdian just a tad longer than the shortest slope. The shortest slope is a lens space filling. On the other hand, there appears to be no such examples (where the meridian isn't shortest) for knots up to 16 crossings. | |
| Aug 30, 2011 at 14:47 | vote | accept | John Pardon | ||
| Aug 5, 2011 at 4:09 | comment | added | Ryan Budney | @Jim: Do they appear in one of the reasonably small censi of knots? If so, it shouldn't take long to find it with a python script. | |
| Aug 5, 2011 at 3:11 | comment | added | Jim Conant | FWIW I just asked Morwen Thistlethwaite about this, and he told me there are examples where the meridian isn't shortest | |
| Aug 5, 2011 at 2:30 | comment | added | Ryan Budney | I believe it's known that the meridian of the knot is usually (or perhaps always) the shortest curve in the cusp. | |
| Aug 5, 2011 at 2:28 | comment | added | Ryan Budney | Yes, many people have studied this. I believe it's commonly referred to as the "cusp shape". I imagine Ian Agol will come along and have something to say, but it's a standard thing to study. Google "hyperbolic knot cusp shape" and you'll get plenty of relevant papers. | |
| Aug 5, 2011 at 2:26 | answer | added | Autumn Kent | timeline score: 12 | |
| Aug 5, 2011 at 1:59 | history | asked | John Pardon | CC BY-SA 3.0 |