@article{c410695d7ca04d929115d2bfdf03620b,

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, intersection multiplicity, Jordan curves, Laurent polynomials, resultant, self-intersections, trigonometric polynomials",

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

note = "Funding Information: Received by the editors February 6, 2019. 2020 Mathematics Subject Classification. Primary 30B60; Secondary 12D10, 42A05. Key words and phrases. Jordan curves, Laurent polynomials, trigonometric polynomials, self-intersections, Bezout theorem, resultant, intersection multiplicity. The first author was supported by SJTU start-up grant program WF220407115 and partially by Russian Foundation for Basic Research (grant 18-31-00101). The second author was supported by the National Science Foundation grants DMS-1362453 and DMS-1764266. Publisher Copyright: {\textcopyright} 2022 American Mathematical Society.",

year = "2023",

month = feb,

doi = "10.1090/proc/14594",

language = "English (US)",

volume = "151",

pages = "547--554",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "2",

}