TL;DR
This paper explores the problem of packing links in Euclidean space to maximize density under geometric constraints, focusing on homotopically essential links and establishing upper bounds.
Contribution
It introduces the problem of packing links with topological considerations and provides initial upper bounds for homotopically essential links.
Findings
Upper bounds for packing densities of homotopically essential links
Highlighting the gap between bounds and potential optimal packings
Encouraging further research into topological packing problems
Abstract
This note initiates an investigation of packing links into a region of Euclidean space to achieve a maximal density subject to geometric constraints. The upper bounds obtained apply only to the class of homotopically essential links and even there seem extravagantly large, leaving much working room for the interested reader.
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Taxonomy
TopicsMathematics and Applications