  We use the polygon representation of 2+1--dimensional gravity to explicitly
carry out the canonical quantization of a universe with the topology of a
torus. The mapping-class-invariant wave function for a quantum ''big bounce'',
is reminiscent of the interference patterns of linear gratings. We consider the
``problem of time'' of quantum gravity: for one choice of internal time the
universe recovers a semiclassical interpretation after the bounce, with a wave
packet centered at a single geometry; for another choice of internal time, the
quantum solutions involve interference between macroscopically distinct
universes.
