The Virtual Spectrum of Linkoids and Open Curves in 3-space
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.
Cite
@article{arxiv.2310.11032,
title = {The Virtual Spectrum of Linkoids and Open Curves in 3-space},
author = {Kasturi Barkataki and Louis H. Kauffman and Eleni Panagiotou},
journal= {arXiv preprint arXiv:2310.11032},
year = {2023}
}