  A 3d generally covariant field theory having some unusual properties is
described. The theory has a degenerate 3-metric which effectively makes it a 2d
field theory in disguise. For 2-manifolds without boundary, it has an infinite
number of conserved charges that are associated with graphs in two dimensions
and the Poisson algebra of the charges is closed. For 2-manifolds with boundary
there are additional observables that have a Kac-Moody Poisson algebra. It is
further shown that the theory is classically integrable and the general
solution of the equations of motion is given. The quantum theory is described
using Dirac quantization, and it is shown that there are quantum states
associated with graphs in two dimensions.
