$A_2$ colored polynomials of rigid vertex graphs

Wataru Yuasa

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arXiv · 1708.09131

$A_2$ colored polynomials of rigid vertex graphs

Wataru Yuasa

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Abstract

The Kauffman-Vogel polynomials are three variable polynomial invariants of $4$-valent rigid vertex graphs. A one-variable specialization of the Kauffman-Vogel polynomials for unoriented $4$-valent rigid vertex graphs was given by using the Kauffman bracket and the Jones-Wenzl idempotent colored with $2$. Bataineh, Elhamdadi and Hajij generalized it to any color with even positive integers. We give another generalization of the one-variable Kauffman-Vogel polynomial for oriented and unoriented $4$-valent rigid vertex graphs by using the $A_2$ bracket and the $A_2$ clasps. These polynomial invariants are considered as the $\mathfrak{sl}_3$ colored Jones polynomials for singular knots and links.

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BibTeX RIS

Wataru Yuasa. 2017-08-30. $A_2$ colored polynomials of rigid vertex graphs. https://arxiv.org/abs/1708.09131

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