A NOTE ON THE WEAK SPLITTING NUMBER

The weak splitting number wsp(L) of a link L is the minimal number of crossing changes needed to turn L into a split union of knots. We describe conditions under which certain R-valued link invariants give lower bounds on wsp(L). This result is used both to obtain new bounds on wsp(L) in terms of the multivariable signature and to recover known lower bounds in terms of the tau and s-invariants. We also establish new obstructions using link Floer homology and apply all these methods to compute wsp for all but two of the 130 prime links with nine or fewer crossings.