  We study the topology of fluid interfaces in the 3D Ising model in the rough
phase. It turns out that such interfaces are accurately described as dilute
gases of microscopic handles, and the stiffness of the interface increases with
the genus. The number of configurations of genus $g$ follows a Poisson-like
distribution. The probability per unit area for creating a handle is well
fitted in a wide range of the inverse temperature $\beta$ near the roughening
point by an exponentially decreasing function of $\beta$. The procedure of
summing over all topologies results in an effective interface whose squared
width scales logarithmically with the lattice size.
