A note on the Lickorish-Millett-Turaev formula for the Kauffman polynomial

Abstract

We use the idea of expressing a nonoriented link as a sum of all oriented links corresponding to the link to present a short proof of the Lickorish-Millett-Turaev formula for the Kauffman polynomial at $z=-a-a^{-1}$. Our approach explains the observation made by Lickorish and Millett that the formula is the generating function for the linking number of a sublink of the given link with its complementary sublink.

arXiv comment5 pages, 4 figures