Gordian Unlinks

TL;DR

This paper introduces the concept of gordian unlinks, which are links that cannot be separated without altering their length or thickness, and provides the first examples and infinite families of such links.

Contribution

It presents the first known examples of gordian unlinks and constructs infinite families for two or more components, expanding understanding of link complexity.

Findings

First examples of gordian unlinks provided

Infinite families of 2-component gordian unlinks constructed

n-component gordian unlinks constructed for all n ≥ 2

Abstract

This paper gives the first examples of gordian unlinks. The components of these unlinks cannot be separated while maintaining constant length and thickness. We construct infinite families of 2-component gordian unlinks and also construct $n$-component gordian unlinks for each $n \geq 2$.