A three-variable transcendental invariant of planar knotoids via Gauss diagrams
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910782429593600 |
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| author | Feng, Wandi Li, Fengling Vesnin, Andrei |
| author_facet | Feng, Wandi Li, Fengling Vesnin, Andrei |
| contents | 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 by using the transcendental invariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19554 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A three-variable transcendental invariant of planar knotoids via Gauss diagrams Feng, Wandi Li, Fengling Vesnin, Andrei Geometric Topology 57K12, 57K35 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 by using the transcendental invariant. |
| title | A three-variable transcendental invariant of planar knotoids via Gauss diagrams |
| topic | Geometric Topology 57K12, 57K35 |
| url | https://arxiv.org/abs/2412.19554 |