Kauffman polynomial

In knot theory, the Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman. It is initially defined on a link diagram as
where formula_2 is the writhe of the link diagram and formula_3 is a polynomial in "a" and "z" defined on link diagrams by the following properties:
Here formula_6 is a strand and formula_7 (resp. formula_8) is the same strand with a right-handed (resp. left-handed) curl added (using a type I Reidemeister move).
Additionally "L" must satisfy Kauffman's skein relation:
The pictures represent the "L" polynomial of the diagrams which differ inside a disc as shown but are identical outside.
Kauffman showed that "L" exists and is a regular isotopy invariant of unoriented links. It follows easily that "F" is an ambient isotopy invariant of oriented links.
The Jones polynomial is a special case of the Kauffman polynomial, as the "L" polynomial specializes to the bracket polynomial. The Kauffman polynomial is related to Chern–Simons gauge theories for SO(N) in the same way that the HOMFLY polynomial is related to Chern–Simons gauge theories for SU(N).