  The linking number (topological entanglement) and the writhe (geometrical
entanglement) of a model of circular double stranded DNA undergoing a thermal
denaturation transition are investigated by Monte Carlo simulations. By
allowing the linking number to fluctuate freely in equilibrium we see that the
linking probability undergoes an abrupt variation (first-order) at the
denaturation transition, and stays close to 1 in the whole native phase. The
average linking number is almost zero in the denatured phase and grows as the
square root of the chain length, N, in the native phase. The writhe of the two
strands grows as the square root of N in both phases.
