Timeline for Is the 4x5 chessboard complex a link complement?
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| Feb 10, 2012 at 2:08 | answer | added | Matthias | timeline score: 16 | |
| Sep 2, 2010 at 7:06 | comment | added | Ryan Budney | If anyone discovers which links this is the complement of, I'd love to find out. | |
| Sep 2, 2010 at 5:49 | history | edited | David Eppstein |
3-manifolds tag
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| Aug 27, 2010 at 22:04 | vote | accept | David Eppstein | ||
| Aug 27, 2010 at 18:16 | comment | added | David Eppstein | The symmetry group should be just the permutations of the rows and columns of the 4x5 grid, S4 x S5. | |
| Aug 27, 2010 at 8:26 | answer | added | Matthias | timeline score: 19 | |
| Aug 27, 2010 at 8:08 | comment | added | Ryan Budney | Ah, 120 regular ideal tetrahedra. Do you know the symmetry group of the triangulation -- could this be something as simple as a 120-sheet cover of the Gieseking manifold? | |
| Aug 27, 2010 at 7:26 | comment | added | Ian Agol | I wouldn't expect this to be a link complement - the cusps are rather large, but the systoles of the cusps aren't large enough to rule out outright. You probably won't find this in any census, since the volume is so big. The first thing to check would be the homology. Unfortunately, although there is an algorithm to check if a cusped manifold is a link complement, it's not very practical to implement. There are finitely curves to check on each cusp, so that any link complement must have one of these curves as a meridian. Then you Dehn fill each possible meridian, regeometrize, and induct. | |
| Aug 27, 2010 at 6:46 | comment | added | Ryan Budney | Can you provide the triangulation? If you have the triangulation handy you can readily write a script (I have one here, if you like) for the python interface to SnapPea, to look for your manifold in the census of link complements. I could e-mail you the script or you could send me the triangulation, whichever you like. | |
| Aug 26, 2010 at 20:25 | history | edited | David Eppstein | CC BY-SA 2.5 |
added 728 characters in body
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| Aug 26, 2010 at 20:05 | comment | added | Joseph O'Rourke | @David, can you provide some reference(s) for chessboard complexes? | |
| Aug 26, 2010 at 18:41 | history | asked | David Eppstein | CC BY-SA 2.5 |