  We attempt to provide a mesoscopic treatment of the origin of black hole
entropy in (3+1)-dimensional spacetimes. We ascribe this entropy to the
non-trivial topology of the space-like sections $\Sigma$ of the horizon. This
is not forbidden by topological censorship, since all the known energy
inequalities needed to prove the spherical topology of $\Sigma$ are violated in
quantum theory. We choose the systoles of $\Sigma$ to encode its complexity,
which gives rise to the black hole entropy. We present hand-waving reasons why
the entropy of the black hole can be considered as a function of the volume
entropy of $\Sigma$. We focus on the limiting case of $\Sigma$ having a large
genus.
