Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
home | mail | papers | authors | news | seminars | events | open positions | login

A. Cavallo - C. Collari - A. Conway

A note on the weak splitting number

created by collari on 14 Nov 2019
modified on 10 Jan 2022


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

ArXiv: 1911.05677 PDF


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.

Credits | Cookie policy | HTML 5 | CSS 2.1