A Three-Variable Transcendental Invariant of Planar Knotoids via Gauss Diagrams Full article
| Journal |
Mediterranean Journal of Mathematics
ISSN: 1660-5446 , E-ISSN: 1660-5454 |
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| Output data | Year: 2025, Volume: 22, Number: 4, Article number : 99, Pages count : 24 DOI: 10.1007/s00009-025-02869-4 | ||||
| Tags | Knotoid, planar knotoid, Gauss diagram, invariants of knotoids, Vassiliev invariant of order one, Gordian distance | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
Abstract:
As a generalization of the classical knots, knotoids are equivalence classes of immersions of the oriented unit interval in a surface. In recent years, a variety of invariants of spherical and planar knotoids have been constructed as extensions of invariants of classical and virtual knots. In this paper, we introduce a three-variable transcendental invariant of planar knotoids which is defined over an index function of a Gauss diagram. We describe properties of this invariant and show that it is a Vassiliev invariant of order one. We also discuss the Gordian distance between planar knotoids and provide lower bounds on the Gordian distance of homotopic planar knotoids using the transcendental invariant.
Cite:
Feng W.
, Li F.
, Vesnin A.
A Three-Variable Transcendental Invariant of Planar Knotoids via Gauss Diagrams
Mediterranean Journal of Mathematics. 2025. V.22. N4. 99 :1-24. DOI: 10.1007/s00009-025-02869-4 WOS Scopus OpenAlex
A Three-Variable Transcendental Invariant of Planar Knotoids via Gauss Diagrams
Mediterranean Journal of Mathematics. 2025. V.22. N4. 99 :1-24. DOI: 10.1007/s00009-025-02869-4 WOS Scopus OpenAlex
Dates:
| Submitted: | Dec 27, 2024 |
| Accepted: | May 27, 2025 |
| Published print: | Jun 10, 2025 |
| Published online: | Jun 10, 2025 |
Identifiers:
| Web of science: | WOS:001505379100001 |
| Scopus: | 2-s2.0-105007602013 |
| OpenAlex: | W4411187894 |
Citing:
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