Email this article Polynomials of complete spatial graphs and Jones polynomial of the related links
- Authors: Vesnin A.Y.1,2,3, Oshmarina O.A.2,3
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Affiliations:
- Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
- Novosibirsk State University, Novosibirsk, Russia
- Tomsk State University, Tomsk, Russia
- Issue: Vol 216, No 5 (2025)
- Pages: 33-63
- Section: Articles
- URL: https://bakhtiniada.ru/0368-8666/article/view/306704
- DOI: https://doi.org/10.4213/sm10167
- ID: 306704
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Abstract
A spatial $K_n$-graph is an embedding of a complete graph $K_n$ with $n$ vertices in a $3$-sphere $S^3$. Knots in a spatial $K_n$-graph corresponding to cycles of $K_n$ are called constituent knots. We consider the case $n=4$. The boundary of the orientable band surface constructed from a spatial $K_4$-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 $K_4$-graphs, their $\theta$-subgraphs and cyclic subgraphs with the Jones polynomials of constituent knots and related links.
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About the authors
Andrei Yurievich Vesnin
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia; Novosibirsk State University, Novosibirsk, Russia; Tomsk State University, Tomsk, Russia
Author for correspondence.
Email: vesnin@math.nsc.ru
Doctor of physico-mathematical sciences, Senior Researcher
Olga Andreevna Oshmarina
Novosibirsk State University, Novosibirsk, Russia; Tomsk State University, Tomsk, Russia
Email: o.oshmarina@g.nsu.ru
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