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

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.

arXiv comment10 pages

References in corpus (1)

• Fourier series of circle embeddings

Cited by in corpus (2)

• Localization of eigenvectors of non-Hermitian banded noisy Toeplitz matrices
• Algebraic structure of the range of a trigonometric polynomial