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On Freedman's link packings

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arxiv 2308.08064 v4 pith:NJYPQRJF submitted 2023-08-15 math.GT math.MG

Fedor Manin , Elia Portnoy This is my paper · ORCID
classification math.GTmath.MG
keywords boundspackingfreedmanlargelinknumberupperarxiv
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Recently, Freedman [arXiv:2301.00295] introduced the idea of packing a maximal number of links into a bounded region subject to geometric constraints, and produced upper bounds on the packing number in some cases, while commenting that these bounds seemed far too large. We show that the smallest of these "extravagantly large" bounds is in fact sharp by constructing, for any link, a packing of exponentially many copies as a function of the available volume. We also produce improved and generalized upper bounds.

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