Modular transformations and one-polygon tessellation

In (2 + 1) gravity, the time evolution of a universe with the spatial topology of a torus can be described by means of a one-polygon tessellation with 3-valent vertices. The action of modular transformations on this solution is considered; it is shown that the corresponding orbit is densely distributed inside the entire phase space of the model. © 1998 Elsevier Science B.V.