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A note on the weak splitting number

MPS-Authors
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Cavallo,  Alberto
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons250160

Collari,  Carlo
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons250165

Conway,  Anthony
Max Planck Institute for Mathematics, Max Planck Society;

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Fulltext (public)

arXiv:1911.05677.pdf
(Preprint), 256KB

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Citation

Cavallo, A., Collari, C., & Conway, A. (2021). A note on the weak splitting number. Proceedings of the American Mathematical Society, 149(3), 1305-1321. doi:10.1090/proc/15177.


Cite as: http://hdl.handle.net/21.11116/0000-0006-E4D7-6
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.