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

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Polynomials of complete spatial graphs and Jones polynomials of the related links. / Vesnin, Andrei Yurievich; Oshmarina, Olga Andreevna.

в: Sbornik Mathematics, Том 216, № 5, 3, 2025, стр. 608-637.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{99b1100e1464422e952b884ddf17413d,

title = "Polynomials of complete spatial graphs and Jones polynomials of the related links",

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.Bibliography: 25 titles.",

keywords = "graph, knot, spatial graph, Jones polynomial, Yamada polynomial, Jaeger polynomial",

author = "Vesnin, {Andrei Yurievich} and Oshmarina, {Olga Andreevna}",

note = "This work was carried out in the framework of the state program of the Scientific and Educational Mathematical Center of Tomsk State University (agreement no. 075-02-2024-1437) and supported by the Ministry of Education and Science of the Russian Federation.",

year = "2025",

doi = "10.4213/sm10167e",

language = "English",

volume = "216",

pages = "608--637",

journal = "Sbornik Mathematics",

issn = "1064-5616",

publisher = "Математический институт им. В.А. Стеклова Российской академии наук (Москва)",

number = "5",

}

RIS

TY - JOUR

T1 - Polynomials of complete spatial graphs and Jones polynomials of the related links

AU - Vesnin, Andrei Yurievich

AU - Oshmarina, Olga Andreevna

N1 - This work was carried out in the framework of the state program of the Scientific and Educational Mathematical Center of Tomsk State University (agreement no. 075-02-2024-1437) and supported by the Ministry of Education and Science of the Russian Federation.

PY - 2025

Y1 - 2025

N2 - 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.Bibliography: 25 titles.

AB - 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.Bibliography: 25 titles.

KW - graph

KW - knot

KW - spatial graph

KW - Jones polynomial

KW - Yamada polynomial

KW - Jaeger polynomial

UR - https://www.scopus.com/pages/publications/105012516684

UR - https://www.elibrary.ru/item.asp?id=82617809

UR - https://www.mendeley.com/catalogue/d049c014-0f0f-3835-8980-b0bbba4e471f/

U2 - 10.4213/sm10167e

DO - 10.4213/sm10167e

M3 - Article

VL - 216

SP - 608

EP - 637

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 5

M1 - 3

ER -

ID: 68732824