Timeline for Some mid-sized ¿hyperbolic? manifolds and SnapPea
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 16, 2012 at 23:48 | comment | added | Nathan Dunfield | @Ryan: My code isn't deterministic. There's random simplifications in constructing the finite triangulation, and a random choice of edge in that triangulation as a new knot. For tri12, I had to randomize stuff a bunch times before finding a description w/o negatively oriented tetrahedra. (Unlike degenerate tetrahedra, which have shape parameter 0, 1, or infinity, negatively oriented tetrahedra are usually harmless in this context.) | |
| Nov 16, 2012 at 22:49 | vote | accept | Ryan Budney | ||
| Nov 16, 2012 at 22:43 | comment | added | Ryan Budney | I can also duplicate your outcome on tri12, identifying it as m032(5,2) but my solution_type always has negatively oriented tetrahedra. | |
| Nov 16, 2012 at 22:22 | comment | added | Ryan Budney | Hi Nathan, strangely if I attempt your filled_triangulation()._to_string() construction in SnapPy, I continue to get negatively-oriented tetrahedra in my solution_type(). I'm using version 1.7 of SnapPy in Ubuntu. But after randomizing the triangulation and repeating, I get your outcome on the nose. Thanks. | |
| Nov 16, 2012 at 17:31 | comment | added | Nathan Dunfield | @Neil: The methods "randomize" and "simplify" preserve the underlying Dehn filling description of the closed manifold, ans so correspond to retriangulating the fixed cusped manifold involved. M.filled_triangulation is a non-ideal 1-vertex triangulation of M which SnapPy can't really work with directly, at least for finding geometric structures. The hackish code Manifold(blah._to_string()) reopens that manifold in SnapPy, which requires it to choose a Dehn filling description of the manifold; it does this by picking at random an edge of the finite triangulation. | |
| Nov 16, 2012 at 11:56 | comment | added | Neil Hoffman | @Nathan: What does "N=Manifold(M.filled_triangulation()._to_string())" do that N.randomize() and N.simplify() don't? | |
| Nov 16, 2012 at 6:19 | comment | added | Ryan Budney | Thanks Nathan. I think I've found the incompressible tori in the 3rd manifold. So I should know the answer to that question soon. | |
| Nov 16, 2012 at 1:50 | history | edited | Nathan Dunfield | CC BY-SA 3.0 |
added 11 characters in body
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| Nov 16, 2012 at 1:10 | history | answered | Nathan Dunfield | CC BY-SA 3.0 |