A note on the weak splitting number

Abstract

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