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On Thickness and Packing Density for Knots and Links

Rob Kusner
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Abstract

We describe some problems, observations, and conjectures concerning thickness and packing density of knots and links in $\sp^3$ and $\R^3$. We prove the thickness of a nontrivial knot or link in $\sp^3$ is no more than $\fracπ{4}$, the thickness of a Hopf link. We also give arguments and evidence supporting the conjecture that the packing density of thick links in $\R^3$ or $\sp^3$ is generally less than $\fracπ{\sqrt{12}}$, the density of the hexagonal packing of unit disks in $\R^2$.

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Rob Kusner. 2002-03-28. On Thickness and Packing Density for Knots and Links. https://arxiv.org/abs/math/0203285

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