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Polynomials of complete spatial graphs and Jones polynomials of the related links Full article

Journal Sbornik Mathematics
ISSN: 1064-5616 , E-ISSN: 1468-4802
Output data Year: 2025, Volume: 216, Number: 5, Pages: 608-637 Pages count : 30 DOI: 10.4213/sm10167e
Tags graph, knot, spatial graph, Jones polynomial, Yamada polynomial, Jaeger polynomial.
Authors Vesnin Andrei Yurievich 1,2,3 , Oshmarina Olga Andreevna 1,3
Affiliations
1 Novosibirsk State University, Novosibirsk, Russia
2 Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
3 Tomsk State University, Tomsk, Russia

Funding (1)

1 Министерство науки и высшего образования РФ 075-02-2024-1437

Abstract: A spatial Kn-graph is an embedding of a complete graph Kn with n vertices in a 3-sphere S3. Knots in a spatial Kn-graph corresponding to cycles of Kn are called constituent knots. We consider the case n = 4. The boundary of the orientable band surface constructed from a spatial K4-graph and having the zero Seifert form is a 4-component link, which is referred to as the associated link. We obtain formulae relating the normalized Yamada and Jaeger polynomials of spatial K4-graphs, their θ-subgraphs and cyclic subgraphs with the Jones polynomials of constituent knots and related links.
Cite: Vesnin A.Y. , Oshmarina O.A.
Polynomials of complete spatial graphs and Jones polynomials of the related links
Sbornik Mathematics. 2025. V.216. N5. P.608-637. DOI: 10.4213/sm10167e Scopus OpenAlex
Original: Веснин А.Ю. , Ошмарина О.А.
Полиномы пространственных полных графов и полиномы Джонса связанных с ними зацеплений
Математический сборник. 2025. Т.216. №5. С.33-63. DOI: 10.4213/sm10167 РИНЦ OpenAlex
Dates:
Submitted: Jul 31, 2024
Identifiers:
Scopus: 2-s2.0-105012516684
OpenAlex: W4413075742
Citing: Пока нет цитирований
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