An infinite family of convex Brunnian links in $R^n$

TL;DR

This paper constructs explicit examples of convex Brunnian links in all dimensions three and higher, extending the concept of Borromean rings to higher-dimensional spaces.

Contribution

It introduces the first explicit constructions of convex Brunnian links in any dimension greater than or equal to three.

Findings

Convex Brunnian links exist in all dimensions n ≥ 3.

Explicit examples of three-component convex Brunnian links are provided.

These links generalize the classical Borromean rings to higher dimensions.

Abstract

This paper proves that convex Brunnian links exist for every dimension $n \geq 3$ by constructing explicit examples. These examples are three-component links which are higher-dimensional generalizations of the Borromean rings.