Nonribbon 2-links all of whose components are trivial knots and some of whose band-sums are nonribbon knots

TL;DR

This paper constructs a specific example of a nonribbon 2-link with trivial components where a band-sum results in a nonribbon 2-knot, illustrating complex behaviors in knot theory.

Contribution

It provides an explicit example of a nonribbon 2-link with trivial components and a nonribbon band-sum, highlighting intricate properties of 2-knots and links.

Findings

Existence of nonribbon 2-links with trivial components

A band-sum of such links can produce a nonribbon 2-knot

Illustrates complex interactions in 2-knot theory

Abstract

There is a nonribbon 2-link all of whose components are trivial 2-knots and one of whose band-sums is a nonribbon 2-knot.