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On a Family of Hyperbolic Brunnian Links and Their Volumes

In: Essays on Topology

Author

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  • Dušan D. Repovš

    (University of Ljubljana & Institute of Mathematics, Physics and Mechanics, Faculty of Education, Faculty of Mathematics and Physics)

  • Andrei Yu. Vesnin

    (Russian Academy of Sciences, Sobolev Institute of Mathematics
    Tomsk State University, Regional Mathematical Center)

Abstract

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 ≥ 2 , $$n\geq 2,$$ we introduce an infinite family of n-component Brunnian links with positive integer parameters Br ( k 1 , … , k n ) $$Br(k_1, \ldots , k_n)$$ that generalize examples constructed by Debrunner in 1964. We are interested in hyperbolic invariants of 3-manifolds S 3 ∖ Br ( k 1 , … , k n ) $$S^3 \setminus Br(k_1, \ldots , k_n)$$ 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.

Suggested Citation

  • Dušan D. Repovš & Andrei Yu. Vesnin, 2025. "On a Family of Hyperbolic Brunnian Links and Their Volumes," Springer Books, in: Louis Funar & Athanase Papadopoulos (ed.), Essays on Topology, chapter 0, pages 495-503, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-81414-3_21
    DOI: 10.1007/978-3-031-81414-3_21
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