Well, billiards humor is a fascinating subject, isn't it? I'm not sure this next piece comes under the heading of pool humor--or does it?

Pool jokes are lovely things where you can find them, but this billiards humor is incidental...

U-Dual Modular Group reports under the heading of "Coxeter Group Structure of Cosmological Billiards on Compact Spatial Manifolds" to present:

"...a systematic study of the cosmological billiard structures of Einstein-p-form systems in which all spatial directions are compactified on a manifold of nontrivial topology.


This is achieved for all maximally oxidised theories associated with split real forms, for all possible compactifications as defined by the de Rham cohomology of the internal manifold. In each case, [the researchers] study the Coxeter group that controls the dynamics for energy scales below the Planck scale as well as the relevant billiard region..."

Do remember, however, that for generic topologies on of the possibilities is that the "...billiard region may or may not be a fundamental domain." Bear in mind, too, that "...the reflections in the billiard walls provide a non-standard presentation of the Coxeter group... it is only when the Coxeter group is a simplex Coxeter group, and the billiard region is a fundamental domain, that there is a correspondence between billiard walls and simple roots of a Kac-Moody algebra, as in the general BKL analysis."

Of course! And certainly as also reported, "For each compactification [the researchers] also determine whether or not the resulting theory exhibits chaotic dynamics."

And to think, all this time I was merely hitting the white cue ball into the colored ones to play pool and billiards! Source: U-Dual Modular Group