Classical N-particle cosmology in 2+1 dimensions

Abstract

In 2+1 dimensional cosmology particles are topological defects in a universe that is nearly everywhere flat. The author uses a time dependent triangulation procedure of space to formulate the laws of evolution and to construct the phase space of this system. A theorem is derived from which it follows that many configurations may have a big bang in their past or a big crunch in their future. The dimensionality of phase space for N particles is 4N-11+12g, where g is the genus of 2-space. This suggests to consider 2N-6+6g pairs of canonical variables and one time variable. The quantum version of this model is speculated about.