Dear Michel,
in the last two years I went more deeply in hyperbolic geometric (hyperbolic 3-manifolds). Then I found many interesting relations to finite groups (of course much of it is also covered by a book of Kapovich "Hyperbolic 3-manifolds and discrete groups"). Together with my coauthor Jerzy, we calculated the partition function of a certain quantum field theory and found quasimodular behavior. Then we started to go into it more deeply and again found interesting relations to finite groups (Fuchsian groups). Then we managed to find a folaition of an exotic R^4 and this foliation is given by tessalation of a hyperbolic disk. Here, I found also your picture.
Your essay opened my eyes and it was like a missing link to fulfill another goal of us: to get a geometric description of quantum mechanics (right along your way).
For my there are many really deep thoughts in your essay and I certainly need moer time to grasp them.
Very good work,
Excited greetings
Torsten