  What can we learn about quantum gravity from a simple toy model, without
actually quantizing it? The toy model consists of a finite number of point
particles, coupled to three dimensional Einstein gravity. It has finitely many
physical degrees of freedom. These are basically the relative positions of the
particles in spacetime and the conjugate momenta. The resulting reduced phase
space is derived from Einstein gravity as a topological field theory. The
crucial point is thereby that we do not make any a priori assumptions about
this phase space, except that the dynamics of the gravitational field is
defined by the Einstein Hilbert action. This already leads to some interesting
features of the reduced phase space, such as a non-commutative structure of
spacetime when the model is quantized.
