# Homotopy ribbon concordance and Alexander polynomials

## TL;DR

This paper proves that homotopy ribbon concordance between links in the 3-sphere imposes divisibility relations on their Alexander polynomials, revealing a new algebraic constraint in knot theory.

## Contribution

It establishes a novel divisibility property of Alexander polynomials under homotopy ribbon concordance, linking geometric concordance to algebraic invariants.

## Key findings

- Alexander polynomial of L divides that of J when J is homotopy ribbon concordant to L
- Provides algebraic constraints for homotopy ribbon concordance
- Enhances understanding of link invariants in concordance theory

## Abstract

We show that if a link J in the 3-sphere is homotopy ribbon concordant to a link L then the Alexander polynomial of L divides the Alexander polynomial of J.