Timeline for SnapPy isometry routine
Current License: CC BY-SA 4.0
12 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Apr 18, 2019 at 23:25 | comment | added | SashaKolpakov | @RyanBudney: great info! Apparently it's different in SnapPea (or may be I misunderstood the C code -- that's highly possible my mistake). Thanks again! | |
| Apr 18, 2019 at 22:44 | comment | added | Ryan Budney | Found it, makeDoubleCover(). If your original non-orientable manifold has tetrahedra 0,1,...,n-1, then the double cover with have tetrahedra 0,1,...,2n-1, and the translate of the i-th tetrahedron will be the i+n-th tetrahedron. | |
| Apr 18, 2019 at 22:36 | comment | added | Ryan Budney | Does Regina have an orientation cover routine? I don't see one in the docs. But perhaps I'm looking in the wrong location. Usually for constructions like this, the ordering of the simplices is described in the documentation. I would imagine they are either side-by-side, or the "bottom" simplices are all first, and their translates appear after that, in the same relative order as in the original triangulation. If you can find the routine, let me know and I can tell you how it works. | |
| Apr 18, 2019 at 22:18 | comment | added | SashaKolpakov | @RyanBudney: Another (may be stupid) question: if N is a non-orientable triangulation, and M is its orientation cover, how are the pre-images of tetrahedron i in N numbered in M? 2*i - 1 and 2*i? Or it's a more complicated numbering? Having such things traceable would be extremely helpful even without more advanced functions, when it comes to see quotients of manifolds by their symmetries, etc, I think. | |
| Apr 18, 2019 at 20:12 | comment | added | SashaKolpakov | @RyanBudney: Good to know. Thanks, Ryan! | |
| Apr 18, 2019 at 19:48 | comment | added | Ryan Budney | Yes, you can. In regina an ideal triangulation is just a triangulation where some of the vertex links are surfaces beyond spheres or discs. So in a cusped hyperbolic 3-manifold they would be tori or klein bottles. So all you have to do is check which vertices are ideal (there is the isIdeal() call) to see how they are permuted. To check if you have a translation action or mirror reflection you'll have to do a little work as Regina does not find the geometric structure on the cusp, but it's certainly a managable task. | |
| Apr 18, 2019 at 9:07 | vote | accept | SashaKolpakov | ||
| Apr 18, 2019 at 7:33 | comment | added | SashaKolpakov | @RyanBudney: Hi Ryan, thanks for your reply. In Regina, however, can I also see the action of those isomorphisms on the cusps? The finicky thing is that I need to see both :-P | |
| Apr 18, 2019 at 4:37 | answer | added | Sam Nead | timeline score: 4 | |
| Apr 18, 2019 at 3:00 | comment | added | Ryan Budney | Yes, there is. I'm not as familiar with the Python interface to SnapPy. There could be something there for you (but I don't see it in the docs). In the underlying C code you have access to how the tetrahedra are permuted. One not-too-pretty way to get access to what you want (this is what I use) is to retriangulate to the canonical triangulation. Save the canonical triangulation, load it into Regina, then call findAllIsomorphisms(). | |
| Apr 17, 2019 at 20:38 | history | asked | SashaKolpakov | CC BY-SA 4.0 |