# Ribbon distance and Khovanov homology

## TL;DR

This paper introduces a new way to measure how close two knots are using ribbon concordances and establishes a lower bound on this distance via Khovanov homology's X-action.

## Contribution

It develops a novel lower bound on ribbon distance between knots based on Khovanov homology, linking knot concordance and homological invariants.

## Key findings

- Lower bound on ribbon distance using Khovanov homology.
- Connection between ribbon concordances and homological invariants.
- Application of Lee's perturbation in bounding knot distances.

## Abstract

We study a notion of distance between knots, defined in terms of the number of saddles in ribbon concordances connecting the knots. We construct a lower bound on this distance using the X-action on Lee's perturbation of Khovanov homology.