# Concordance to links with an unknotted component

## TL;DR

This paper constructs complex links with all components slice that cannot be simplified to links with an unknotted component, using Alexander modules as the main tool.

## Contribution

It introduces a novel method to distinguish links with all slice components from those with unknotted components, expanding understanding of link concordance.

## Key findings

- Links with all slice components are not necessarily concordant to links with unknotted components.
- Alexander modules can effectively distinguish complex link concordance classes.
- The construction works for links with arbitrarily many components.

## Abstract

We construct links of arbitrarily many components each component of which is slice and yet are not concordant to any link with even one unknotted component. The only tool we use comes from the Alexander modules.