Flexible, randomly triangulated, self-avoiding surfaces are studied by
Monte Carlo simulation technique. The surfaces are closed, but handle
s can spontaneously be formed or annihilated. The simulations lead to
estimates for the exponents relating area, enclosed volume and number
of handles to the extension of the surface: d(A) = 1.94, d(V) = 1.96,
d(chi) = 2.0. The results obtained suggest that free topology is irrel
evant when classifying fluid self-avoiding surfaces in terms of univer
sality classes.