A note on the weak splitting number

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