  We show that two open books in a given closed, oriented three-manifold admit
isotopic stabilizations, where the stabilization is made by successive
plumbings with Hopf bands, if and only if their associated plane fields are
homologous. Since this condition is automatically fulfilled in an integral
homology sphere, the theorem implies a conjecture of J Harer, namely, that any
fibered link in the three-sphere can be obtained from the unknot by a sequence
of plumbings and deplumbings of Hopf bands. The proof presented here involves
contact geometry in an essential way.
