On a state model for the $\mathrm{SO}(2n)$ Kauffman polynomial

Abstract

François Jaeger presented the two-variable Kauffman polynomial of an unoriented link $L$ as a weighted sum of HOMFLY-PT polynomials of oriented links associated with $L$. Murakami, Ohtsuki and Yamada (MOY) used planar graphs and a recursive evaluation of these graphs to construct a state model for the $sl\left(n\right)$-link invariant (a one-variable specialization of the HOMFLY-PT polynomial). We apply the MOY framework to Jaeger’s work, and construct a state summation model for the $SO\left(2n\right)$ Kauffman polynomial.