Compact phase space, cosmological constant, and discrete time

We study the quantization of geometry in the presence of a cosmological constant, using a discretization with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to the discreteness of time, in addition to space. We work in $2+1$ dimensions, but these results may be relevant also for the physical $3+1$ case.