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Sep 24, 2013 at 9:18 comment added Elbabak The interest of using Klein's model is precisely to avoid to explain this (see [BPS])! But it is not so difficult to guess what are the shear coordinates in Poincaré's model $\mathbb D$. For any 2-face (euclidean triangle) $T$ of ${\cal D}(S,g)$, one associates an ideal triangle $h(T)$ in $\mathbb D$. Given two adjacent such triangles $T_1=ABC$ and $T_2=ABD$ on the surface, one defines $r(T_1,T_2)=\log(\lvert AC\lvert \lvert BD\lvert/\lvert BC \lvert \lvert AD \lvert )$. It is the shear coordinate used in [R] to glue together $h(T_1)$ and $h(T_2)$.
Sep 24, 2013 at 9:05 vote accept Elbabak
Sep 23, 2013 at 14:35 answer added Igor Rivin timeline score: 3
Sep 23, 2013 at 14:19 comment added Jean Raimbault How exactly do you choose the shear coordinates used for the gluing? (I will readily admit I am too lazy to go to the original reference to find it out.)
Sep 23, 2013 at 13:17 review First posts
Sep 23, 2013 at 13:32
Sep 23, 2013 at 13:05 history edited Elbabak CC BY-SA 3.0
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Sep 23, 2013 at 12:58 history asked Elbabak CC BY-SA 3.0