# Self-intersections of Laurent polynomials and the density of Jordan curves

## TL;DR

This paper extends bounds on self-intersections from polynomial to Laurent polynomial curves and demonstrates that circle embeddings are dense among all planar circle maps.

## Contribution

It generalizes Quine's bound to Laurent polynomials and proves the density of circle embeddings in the space of all circle-to-plane maps.

## Key findings

- Extended Quine's bound to Laurent polynomial curves
- Proved density of circle embeddings among all circle maps
- Applicable to understanding curve self-intersections and embeddings

## Abstract

We extend Quine's bound on the number of self-intersection of curves with polynomial parameterization to the case of Laurent polynomials. As an application, we show that circle embeddings are dense among all maps from a circle to a plane with respect to an integral norm.