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The virtual spectrum of linkoids and open curves in 3-space

School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85281, USA

Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7045, USA

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Eleni Panagiotou

https://orcid.org/0000-0002-1655-6447

School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85281, USA

Corresponding author.

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https://doi.org/10.1142/S0218216524500068Cited by:0 (Source: Crossref)

Abstract

The entanglement of open curves in 3-space appears in many physical systems and affects their material properties and function. A new framework in knot theory was introduced recently, that enables to characterize the complexity of collections of open curves in 3-space using the theory of knotoids and linkoids, which are equivalence classes of diagrams with open arcs. In this paper, new invariants of linkoids are introduced via a surjective map between linkoids and virtual knots. This leads to a new collection of strong invariants of linkoids that are independent of any given virtual closure. This gives rise to a collection of novel measures of entanglement of open curves in 3-space, which are continuous functions of the curve coordinates and tend to their corresponding classical invariants when the endpoints of the curves tend to coincide.

Keywords:

AMSC: 57K12

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