# Distortion and the bridge distance of knots

## TL;DR

This paper establishes a lower bound on the distortion of knots in three-dimensional space based on bridge distance and bridge number, providing new insights into knot complexity and geometric properties.

## Contribution

The paper extends Pardon's techniques to relate knot distortion with bridge distance and bridge number, introducing an infinite family of knots with unbounded bridge parameters and constant lower bounds.

## Key findings

- Lower bound on knot distortion proportional to bridge distance and bridge number
- Existence of knots with unbounded bridge parameters and constant distortion bounds
- Extension of Pardon's techniques to new knot invariants

## Abstract

We extend techniques due to Pardon to show that there is a lower bound on the distortion of a knot in $\mathbb{R}^3$ proportional to the minimum of the bridge distance and the bridge number of the knot. We also exhibit an infinite family of knots for which the minimum of the bridge distance and the bridge number is unbounded and Pardon's lower bound is constant.