On a family of hyperbolic Brunnian links and their volumes

Repovš, Dušan (author), Vesnin, Andreî Jurʹevič (author)

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.

• Language: English
• Keywords: hyperbolic Brunnian link, Adams move, augmented link, ideal right-angled antiprism
• Work type: Other
• Typology: 1.16 - Independent Scientific Component Part or a Chapter in a Monograph
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication version: Author Accepted Manuscript
• Year: 2025
• Number of pages: Str. 495-503
• PID: 20.500.12556/RUL-182449
• UDC: 515.1
• COBISS.SI-ID: 244039171
• Publication date in RUL: 12.05.2026

Record is a part of a monograph

• Title: Essays on topology : dedicated to Valentin Poénaru
• Editors: Louis Funar, Athanase Papadopoulos
• Place of publishing: Cham
• Publisher: Springer
• ISBN: 978-3-031-81413-6
• COBISS.SI-ID: 244025347