On a family of hyperbolic Brunnian links and their volumes
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| Format: | Preprint |
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2025
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| _version_ | 1866909704909750272 |
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| author | Repovš, Dušan D. Vesnin, Andrei Yu. |
| author_facet | Repovš, Dušan D. Vesnin, Andrei Yu. |
| contents | An $n$-component link $L$ is said to be \emph{Brunnian} if it is non-trivial but every proper sublink of $L$ is trivial. The simplest and best known example of a hyperbolic Brunnian link is the 3-component link known as "Borromean rings". For $n\geq 2,$ we introduce an infinite family of $n$-component Brunnian links with positive integer parameters $Br(k_1, \ldots, k_n)$ that generalize examples constructed by Debrunner in 1964. We are interested in hyperbolic invariants of 3-manifolds $S^3 \setminus Br(k_1, \ldots, k_n)$ and we obtain upper bounds for their volumes. Our approach is based on Dehn fillings on cusped manifolds with volumes related to volumes of ideal right-angled hyperbolic antiprisms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_17974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a family of hyperbolic Brunnian links and their volumes Repovš, Dušan D. Vesnin, Andrei Yu. Geometric Topology Metric Geometry 57K10, 57K32, 52B10 An $n$-component link $L$ is said to be \emph{Brunnian} if it is non-trivial but every proper sublink of $L$ is trivial. The simplest and best known example of a hyperbolic Brunnian link is the 3-component link known as "Borromean rings". For $n\geq 2,$ we introduce an infinite family of $n$-component Brunnian links with positive integer parameters $Br(k_1, \ldots, k_n)$ that generalize examples constructed by Debrunner in 1964. We are interested in hyperbolic invariants of 3-manifolds $S^3 \setminus Br(k_1, \ldots, k_n)$ and we obtain upper bounds for their volumes. Our approach is based on Dehn fillings on cusped manifolds with volumes related to volumes of ideal right-angled hyperbolic antiprisms. |
| title | On a family of hyperbolic Brunnian links and their volumes |
| topic | Geometric Topology Metric Geometry 57K10, 57K32, 52B10 |
| url | https://arxiv.org/abs/2503.17974 |