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The virtual spectrum of linkoids and open curves in 3-space.
- Source :
-
Journal of Knot Theory & Its Ramifications . Mar2024, Vol. 33 Issue 3, p1-33. 33p. - Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *KNOT theory
*CONTINUOUS functions
Subjects
Details
- Language :
- English
- ISSN :
- 02182165
- Volume :
- 33
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Knot Theory & Its Ramifications
- Publication Type :
- Academic Journal
- Accession number :
- 178066776
- Full Text :
- https://doi.org/10.1142/S0218216524500068