New York Journal of Mathematics
Volume 24 (2018), 355-374


Wataru Yuasa

A2 colored polynomials of rigid vertex graphs

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Published: June 20, 2018
Keywords: Kauffman--Vogel polynomials, Colored Jones polynomials, Skein theory.
Subject: 57M27

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 with the color 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 A2 bracket and the A2 clasps. These polynomial invariants are considered as the $\mathfrak{sl}_3$ colored Jones polynomials for singular knots and links.


The author would like to express his gratitude to his adviser, Hisaaki Endo, for his encouragement.

Author information

Wataru Yuasa:
Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan