  We demonstrate a variant of the Bond Fluctuation lattice Monte Carlo model in
which moves through cis conformations are forbidden. Ring polymers in this
model have a conserved quantity that amounts to a topological linking number.
Increased linking number reduces the radius of gyration mildly. A linking
number of order 0.2 per bond leads to an eight-percent reduction of the radius
for 128-bond chains. This percentage appears to rise with increasing chain
length, contrary to expectation. For ring chains evolving without the
conservation of linking number, we demonstrate a substantial anti-correlation
between the twist and writhe variables whose sum yields the linking number. We
raise the possibility that our observed anti-correlations may have counterparts
in the most important practical polymer that conserves linking number, DNA.
