An infinite family of convex Brunnian links in \({\mathbb{R}^n}\) (Q715264)

The authors construct explicit examples of convex Brunnian links in \(\mathbb{R}^n\) for \(n \geq 3\). These examples are higher-dimensional generalizations of the Borromean rings, and they give an affirmative answer to a question asked by \textit{H. N. Howards} [Am. Math. Mon. 115, No. 2, 114--124 (2008; Zbl 1148.57302)]. Let us review the main terms. A knot in \(\mathbb{R}^n\) is a subset of \(\mathbb{R}^n\) homeomorphic to a \(k\)-dimensional sphere for some \(k\), and a link is a disjoint union of finitely many knots (possibly of different dimensions). A link is said to be convex if each component bounds a ball which is convex. A Brunnian link is a link with three or more than three components which is not an unlink, but every proper sublink is an unlink; here a link is said to be an unlink if each component bounds a ball which is disjoint from the other components.