Timeline for Change of coordinates for Teichmüller space of the 4-holed sphere
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 24, 2019 at 11:58 | comment | added | giulio bullsaver | Does anyone have a reference for the proof of the above formula other than the original paper? I am not able to find a .pdf of the original paper anywhere... | |
| Jul 12, 2019 at 12:34 | comment | added | giulio bullsaver | I am still very interested in the topic. Something that I found out later is that for some surfaces the pants complex is polytopal: for the simplest surfaces (resp: disk with punctures on a boundary, disk with also one puncture inside, annulus with punctures on a single boundary) one gets (resp: Associahedra, Cyclohedra, Halohedra). The first two clearly match with the cluster algebras of type A, B/C. The halohedron has a combinatorics remarkably similar to that of D, altough with a doubling of facets (see Nima Arkani-Hamed's talk at Amplitudes 2019 or Song He's today at Strings). | |
| Jul 11, 2019 at 4:13 | comment | added | Dylan Thurston | @giuliobullsaver, I just saw this. The lambda-lengths version by Penner is a cluster algebra pretty much on the nose (discovered long before cluster algebras were invented). The pants version in the question & answer looks temptingly algebraic, but I do not know a cluster-algebra-like interpretation (despite trying). | |
| Jul 15, 2018 at 9:09 | comment | added | Sam Nead | I don't know, but perhaps Dylan does. If he doesn't answer here, you should ask him directly. Or better yet: ask on MathOverflow! :) | |
| Jul 14, 2018 at 0:09 | comment | added | giulio bullsaver | Do you think these transformations can be put in a cluster-algebra form? | |
| May 9, 2017 at 10:20 | comment | added | Dylan Thurston | From a pair of pants decomposition of the surface, if you choose an orientation on each pants curve you get a natural spun triangulation. There are coordinates associated to spun triangulations in general. These are close to the Fenchel-Nielsen coordinates, but not quite the same. But then changing the spun triangulation to do the necessary pants move is not obvious. (Which is all to say that Igor's idea is not crazy, but is complicated to work out.) | |
| Feb 9, 2016 at 19:58 | comment | added | Igor Rivin | I think that if you allow spun triangulations (or whatever they are called), everything works fine... | |
| Feb 9, 2016 at 19:49 | comment | added | Sam Nead | @Igor - As far as I understand them, Penner's lambda lengths require that the surface have punctures, and also a choice of ideal triangulation (instead of a pants decomposition). | |
| Mar 2, 2014 at 17:23 | comment | added | Igor Rivin | Hasn't this all been done earlier by Penner, with his Lambda lengths? | |
| S Mar 2, 2014 at 15:48 | history | suggested | Jamie Vicary | CC BY-SA 3.0 |
Added key details from cited paper
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| Mar 2, 2014 at 15:39 | vote | accept | Jamie Vicary | ||
| Mar 2, 2014 at 15:38 | review | Suggested edits | |||
| S Mar 2, 2014 at 15:48 | |||||
| Mar 2, 2014 at 14:24 | history | answered | Sam Nead | CC BY-SA 3.0 |