How Many Links Fit in a Box?
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912283234402304 |
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| author | Freedman, Michael H. |
| author_facet | Freedman, Michael H. |
| contents | In an earlier note [arXiv:2301.00295] it was shown that there is an upper bound to the number of disjoint Hopf links (and certain related links) that can be embedded in the unit cube where there is a fixed separation required between the components within each copy of the Hopf link. The arguments relied on multi-linear properties of linking number and certain other link invariants. Here we produce a very similar upper bound for all non-trivial links by a more-general, entirely geometric, argument (but one which, unlike the original, has no analog in higher dimensions). Shortly after the initial paper, [arXiv:2308.08064] proved lower bounds which still provide a converse to our Theorem 1 in the case that only a bounded number of link types appear among the set $\{L_i\}$ as $N$ increases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02989 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How Many Links Fit in a Box? Freedman, Michael H. Geometric Topology In an earlier note [arXiv:2301.00295] it was shown that there is an upper bound to the number of disjoint Hopf links (and certain related links) that can be embedded in the unit cube where there is a fixed separation required between the components within each copy of the Hopf link. The arguments relied on multi-linear properties of linking number and certain other link invariants. Here we produce a very similar upper bound for all non-trivial links by a more-general, entirely geometric, argument (but one which, unlike the original, has no analog in higher dimensions). Shortly after the initial paper, [arXiv:2308.08064] proved lower bounds which still provide a converse to our Theorem 1 in the case that only a bounded number of link types appear among the set $\{L_i\}$ as $N$ increases. |
| title | How Many Links Fit in a Box? |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2412.02989 |