Published Paper
Inserted: 14 nov 2019
Last Updated: 10 jan 2022
Journal: Proceedings of the AMS
Volume: 149
Number: 3
Pages: 1305–1321
Year: 2021
Doi: 10.1090/proc/15177
Abstract:
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 $\mathbb{R}$-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 $9$ or fewer crossings.