SELF-INTERSECTIONS OF LAURENT POLYNOMIALS AND THE DENSITY OF JORDAN CURVES

Sergei Kalmykov; Leonid V. Kovalev

doi:10.1090/proc/14594

SELF-INTERSECTIONS OF LAURENT POLYNOMIALS AND THE DENSITY OF JORDAN CURVES

Sergei Kalmykov, Leonid V. Kovalev

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English (US)
Pages (from-to)	547-554
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	151
Issue number	2
DOIs	https://doi.org/10.1090/proc/14594
State	Published - Feb 2023

Keywords

Bezout theorem
Jordan curves
Laurent polynomials
intersection multiplicity
resultant
self-intersections
trigonometric polynomials

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/proc/14594

Cite this

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title = "SELF-INTERSECTIONS OF LAURENT POLYNOMIALS AND THE DENSITY OF JORDAN CURVES",

abstract = "We extend Quine{\textquoteright}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.",

keywords = "Bezout theorem, Jordan curves, Laurent polynomials, intersection multiplicity, resultant, self-intersections, trigonometric polynomials",

author = "Sergei Kalmykov and Kovalev, {Leonid V.}",

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year = "2023",

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N2 - 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.

AB - 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.

KW - Bezout theorem

KW - Jordan curves

KW - Laurent polynomials

KW - intersection multiplicity

KW - resultant

KW - self-intersections

KW - trigonometric polynomials

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SELF-INTERSECTIONS OF LAURENT POLYNOMIALS AND THE DENSITY OF JORDAN CURVES

Abstract

Keywords

ASJC Scopus subject areas

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