Timeline for How to flip one triangulation on a surface into another
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 22, 2015 at 7:42 | vote | accept | Mikhail | ||
| Jan 21, 2015 at 22:27 | comment | added | Dylan Thurston | Mikhail, I'm not seeing the issue with Mosher's lemma. I'll follow Mosher and call the new diagonal $h'$. What you say is correct, but the intersections of $h'$ with $h$ are a subset of the intersections of the old edge $h_{SW}$ with $h$. But the intersections of $h_{SW}$ with $h$ are not counted in the new triangulation. | |
| Jan 21, 2015 at 22:24 | comment | added | Dylan Thurston | I strongly suspect, by the way, that it is not possible to do flips that monotonically decrease the total number of intersections between the two triangulations; hence Mosher's weird definition, and also why Lackenby looked at the dual spine. | |
| Jan 21, 2015 at 21:35 | comment | added | Ian Agol | A simple proof of this using a triangulation and a dual spine, performing flips to decrease the intersection number, is given in Lemma 6 of this paper of Lackenby: msp.org/gt/2000/4-1/p12.xhtml I think it ought to be possible to make this proof effective to give an algorithm. | |
| Jan 21, 2015 at 15:00 | history | edited | Mikhail | CC BY-SA 3.0 |
added 568 characters in body
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| Jan 20, 2015 at 22:14 | answer | added | Sam Nead | timeline score: 5 | |
| Jan 20, 2015 at 17:02 | answer | added | Igor Rivin | timeline score: 4 | |
| Jan 20, 2015 at 16:39 | comment | added | Mikhail | Yes, the reference to the Mosher paper was found in the literature about claster algebras. | |
| Jan 20, 2015 at 15:58 | comment | added | Christian Stump | mathoverflow.net/questions/194291 | |
| Jan 20, 2015 at 15:56 | comment | added | Jan Grabowski | Yoive tagged this as cluster-algebras but have you explored the literature there about cluster algebras associated to surfaces? (There was a not entirely unrelated quested here earlier today, but on mobile I can't very easily find and paste the link. Maybe someone helpful could? The poster was @HughThomas.) | |
| Jan 20, 2015 at 15:36 | history | asked | Mikhail | CC BY-SA 3.0 |