  The conformation of circular DNA molecules of various lengths adsorbed in a
2D conformation on a mica surface is studied. The results confirm the
conjecture that the critical exponent $\nu$ is topologically invariant and
equal to the SAW value (in the present case $\nu=3/4$), and that the topology
and dimensionality of the system strongly influences the cross-over between the
rigid regime and the self-avoiding regime at a scale $L\approx 8 \ell_p$.
Additionally, the bond correlation function scales with the molecular length
$L$ as predicted. For molecular lengths $L\leq5 \ell_p$, circular DNA behaves
like a stiff molecule with approximately elliptic shape.
