  We study the XY model on a lattice with fluctuating connectivity. The
expectation is that at an appropriate critical point such a system corresponds
to a compactified boson coupled to 2d quantum gravity. Our simulations focus,
in particular, on the important topological features of the system. The results
lend strong support to the two phase structure predicted on the basis of
analytical calculations. A careful finite size scaling analysis yields
estimates for the critical exponents in the low temperature phase.
