is a polynomial in a and z defined on link diagrams by the following properties: Here
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 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).