Title: On a family of hyperbolic Brunnian links and their volumes Show Chinese title

Title: 关于一类双曲布伦尼亚链环及其体积

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 $Br(k_1, \ldots, k_n)$ 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. Show Chinese abstract

Abstract: 一个$n$-成分链$L$被称为\emph{布伦尼亚an}如果它非平凡但$L$的每一个真子链都是平凡的。 双曲Brunnian链最简单且最著名的例子是三个成分的链，称为“三环链”。 对于$n\geq 2,$我们引入了一个无限族$n$-成分的 Brunnian 链，其正整数参数为$Br(k_1, \ldots, k_n)$，这些链推广了Debrunner在1964年构造的例子。 我们感兴趣的是3-流形$S^3 \setminus Br(k_1, \ldots, k_n)$的双曲不变量，并且我们得到了它们体积的上界。 我们的方法基于带有与理想直角双曲反棱柱体积相关的体积的有柄流形的德恩填充。