On Freedman's link packings
Geometric Topology
2024-10-22 v4 Metric Geometry
Abstract
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.
Cite
@article{arxiv.2308.08064,
title = {On Freedman's link packings},
author = {Fedor Manin and Elia Portnoy},
journal= {arXiv preprint arXiv:2308.08064},
year = {2024}
}
Comments
17 pages, 4 figures. v4 corrects a minor error in the proof of Lemma 3.1. Final version accepted at J. Topol. Anal