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An n-component link L is said to be 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.

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On a Family of Hyperbolic Brunnian Links and Their Volumes

  • 章节

  • 发表日期：

    2025年

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  • Dušan D. Repovš,
  • Andrei Yu. Vesnin

摘要

An n-component link L is said to be 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.