Timeline for Explicit tetrahedralizations of closed 3-manifolds and connections between convex polytopes and hyperbolic knot complements
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 8, 2019 at 16:32 | answer | added | Neil Hoffman | timeline score: 2 | |
| Mar 14, 2012 at 3:02 | vote | accept | Samuel Reid | ||
| Mar 13, 2012 at 17:12 | answer | added | Ryan Budney | timeline score: 7 | |
| Mar 12, 2012 at 1:23 | comment | added | Samuel Reid | @RyanBudney: That is exactly what I would be looking for, could you make your response an answer so I can accept it? | |
| Mar 9, 2012 at 21:23 | comment | added | Ryan Budney | The software "Regina" by Ben Burton has over 16,000 explicit triangulations of 3-manifolds. | |
| Feb 11, 2012 at 17:02 | comment | added | Ian Agol | In case you haven't seen it, I suggest you look at the programs Snappea or SnapPy computop.org They compute Dirichlet domains of hyperbolic manifolds. If the Dirichet domain happens to be generic, then it is dual to a triangulation. For cusped hyperbolic manifolds (such as hyperbolic knot complements), the Ford domain many times gives rise to a canonical triangulation. | |
| Jan 26, 2012 at 5:45 | comment | added | Samuel Reid | @Jim Conant: What if I was interested in an ideal triangulation? Do you happen to know of any literature I could look at or if you know, could you give an explanation? | |
| Jan 20, 2012 at 14:50 | comment | added | Jim Conant | @Samuel: Do you want an ideal triangulation? (Meaning vertices at infinity and edges geodesic.) That's a bit harder. Otherwise, yes you can just look at your manifold as a quotient space of a polyhedron and subdivide. | |
| Jan 20, 2012 at 4:44 | comment | added | Sam Nead | "vertex coordinates of the tetrahedra" -- this doesn't make much sense. In full generality (whatever that means) triangulations are topological objects, not geometric ones. You have to restrict the setting to get to triangulations that have geometric meaning. The standard way to do this, following Thurston, is to consider ideal triangulations of knot complements. There is a discussion of this at the beginning of chapter three of Thurston's book. | |
| Jan 20, 2012 at 3:13 | comment | added | Samuel Reid | @Jim Conant: For constructing the tetrahedralization of a hyperbolic knot complement, I simply perform barycentric subdivision on the fundamental domain? | |
| Jan 20, 2012 at 3:08 | comment | added | Samuel Reid | Thank you for that suggestion, I had not thought of that. | |
| Jan 20, 2012 at 3:00 | comment | added | Jim Conant | Can't you triangulate these dodecahedral manifolds by taking the central subdivision of each face, coning to the center, and then barycentrically subdividing? | |
| Jan 20, 2012 at 2:55 | history | asked | Samuel Reid | CC BY-SA 3.0 |