Milnor invariants and thickness of spherical links
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909768130494464 |
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| author | Komendarczyk, Rafał Koytcheff, Robin Manin, Fedor |
| author_facet | Komendarczyk, Rafał Koytcheff, Robin Manin, Fedor |
| contents | The ropelength of a knot or link is the minimal number of inches of 1-inch-thick rope that it takes to tie it. The relationship of this measurement to knot and link invariants has been studied by various authors. We give the first results of this type for higher-dimensional spherical links, generalizing work of the first author and Michaelides in the classical case. We find optimal asymptotic bounds on their Milnor invariants in terms of thickness, uncovering a dichotomy between a polynomial and an exponential regime. Along the way, we give a detailed treatment of these Milnor invariants and their properties using Massey products. As an application, we resolve a question of Freedman and Krushkal. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_02883 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Milnor invariants and thickness of spherical links Komendarczyk, Rafał Koytcheff, Robin Manin, Fedor Geometric Topology Differential Geometry Metric Geometry 57K45 (Primary), 53C23, 53A07, 55S30, 57Q35 (Secondary) The ropelength of a knot or link is the minimal number of inches of 1-inch-thick rope that it takes to tie it. The relationship of this measurement to knot and link invariants has been studied by various authors. We give the first results of this type for higher-dimensional spherical links, generalizing work of the first author and Michaelides in the classical case. We find optimal asymptotic bounds on their Milnor invariants in terms of thickness, uncovering a dichotomy between a polynomial and an exponential regime. Along the way, we give a detailed treatment of these Milnor invariants and their properties using Massey products. As an application, we resolve a question of Freedman and Krushkal. |
| title | Milnor invariants and thickness of spherical links |
| topic | Geometric Topology Differential Geometry Metric Geometry 57K45 (Primary), 53C23, 53A07, 55S30, 57Q35 (Secondary) |
| url | https://arxiv.org/abs/2509.02883 |