$A_2$ colored polynomials of rigid vertex graphs

Wataru Yuasa

paper

$A_{2}$ colored polynomials of rigid vertex graphs

arXiv:1708.09131

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 $sl_{3}$ colored Jones polynomials for singular knots and links.

15 pages, many TikZ pictures

A2​ colored polynomials of rigid vertex graphs

Abstract

References in corpus (2)

$A_{2}$ colored polynomials of rigid vertex graphs