  We study microstates of the three dimensional black hole obtained by
quantizing topologically non-trivial geometries behind the event horizon. In
chiral gravity these states are found by quantizing the moduli space of
bordered Riemann surfaces. In the semi-classical limit these microstates can be
counted using intersection theory on the moduli space of punctured Riemann
surfaces. We make a conjecture (supported by numerics) for the asymptotic
behaviour of the relevant intersection numbers. The result is that the
geometric microstates with fixed topology have an entropy which grows too
slowly to account for the semiclassical Bekenstein-Hawking entropy. The sum
over topologies, however, leads to a divergence. We conclude with some
speculations about how this might be resolved to give an entropy proportional
to horizon area.
