Dear Torsten,
I am trying to better understand your deep essay but it turns out to be quite difficult accounting for my poor knowledge of differential geometry.
I have a naive question. The (first) Hopf fibration S^3 can be seen as the sphere bundle over the Riemann sphere S^2 with fiber S^1. Could you explain what is the sphere bundle S^2 x [0,1] that you associate to the gravitational interaction? May it be considered as some sort of lift from dessins d'enfants on S^2 to S^2 x S^0, and the latter object lives in circles on S^3, right?
I have in mind Matlock's essay as well.
All the best,
Michel