On a family of hyperbolic Brunnian links and their volumes

Dušan D. Repovš; Andrei Yu. Vesnin

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

paper

On a family of hyperbolic Brunnian links and their volumes

arXiv:2503.17974 · doi:10.1007/978-3-031-81414-3_21

Abstract

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 $B r (k_{1}, \dots, k_{n})$ that generalize examples constructed by Debrunner in 1964. We are interested in hyperbolic invariants of 3-manifolds $S^{3} ∖ B r (k_{1}, \dots, k_{n})$ 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.