A note on the weak splitting number

Cavallo, Alberto; Collari, Carlo; Conway, Anthony

doi:10.1090/proc/15177

A note on the weak splitting number
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by Alberto Cavallo, Carlo Collari and Anthony Conway PDF

Proc. Amer. Math. Soc. 149 (2021), 1305-1321 Request permission

Abstract:

The weak splitting number $\operatorname {wsp}(L)$ 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 $\mathbb {R}$-valued link invariants give lower bounds on $\operatorname {wsp}(L)$. This result is used both to obtain new bounds on $\operatorname {wsp}(L)$ 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 $\operatorname {wsp}$ for all but two of the $130$ prime links with nine or fewer crossings.

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