Polynomials of complete spatial graphs and Jones polynomial of related links

Olga Oshmarina; Andrei Vesnin

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arXiv · 2404.12264

Polynomials of complete spatial graphs and Jones polynomial of related links

Olga Oshmarina·Andrei Vesnin

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Abstract

Let $K_n$ be a complete graph with $n$ vertices. An embedding of $K_n$ in $S^3$ is called a spatial $K_n$-graph. Knots in a spatial $K_n$-graph corresponding to simple cycles of $K_n$ are said to be constituent knots. We consider the case $n=4$. The boundary of an oriented band surface with zero Seifert form, constructed for a spatial $K_4$, is a four-component associated link. There are obtained relations between normalized Yamada and Jaeger polynomials of spatial graphs and Jones polynomials of constituent knots and the associated link.

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Olga Oshmarina, Andrei Vesnin. 2024-04-18. Polynomials of complete spatial graphs and Jones polynomial of related links. https://arxiv.org/abs/2404.12264

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