Timeline for Finding hyperbolic metrics by approximation
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 17, 2012 at 13:25 | vote | accept | HenrikRüping | ||
| Apr 16, 2012 at 21:10 | comment | added | Misha | @Sam: Dear Sam, yes, of course. By the way, to the best of my knowledge, nobody really knows why Snappea works so well and so fast. Casson's (unsuccessful) approach to the geometrization conjecture was an attempt to explain why. Maybe, if there is a combinatorial Ricci flow, it would explain it, but so far there was very little real progress in this direction. | |
| Apr 16, 2012 at 14:47 | comment | added | Sam Nead | Dear Misha - Hence the parenthetical remark near the beginning of my post. (If you will kindly read "not easy" to mean "impossible" ;) | |
| Apr 16, 2012 at 14:45 | history | edited | Sam Nead | CC BY-SA 3.0 |
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| Apr 16, 2012 at 14:37 | comment | added | Misha | @Sam: I think you need a triangulation or something equivalent to it, like Heegaard diagram. If you start with an arbitrary presentation then you would not be find an algorithm for the word problem (even though, you know that one exists). For instance, take the free product of a hyperbolic 3-manifold group (with a nice presentation) with the trivial group that is given an "unrecognizable" presentation. Thus, in this case, one cannot hope for an algorithm for finding a discrete and faithful representation. | |
| Apr 16, 2012 at 14:37 | history | edited | Sam Nead | CC BY-SA 3.0 |
Added remarks about the mystery...
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| Apr 16, 2012 at 14:21 | history | answered | Sam Nead | CC BY-SA 3.0 |