On a Family of Hyperbolic Brunnian Links and Their Volumes

Dušan D. Repovš () and Andrei Yu. Vesnin ()
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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

Chapter Chapter 21 in Essays on Topology, 2025, pp 495-503 from Springer

Abstract: 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.

Keywords: Hyperbolic Brunnian link; Adams move; Augmented link; Ideal right-angled antiprism; 57K10; 57K32; 52B10 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-81414-3_21

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DOI: 10.1007/978-3-031-81414-3_21

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