In the mathematical field of knot theory, the bracket polynomial (also known as the Kauffman bracket) is a polynomial invariant of framed links.
In particular, Kauffman's interpretation of the Jones polynomial allows generalization to invariants of 3-manifolds.
The bracket polynomial was discovered by Louis Kauffman in 1987.
The bracket polynomial of any (unoriented) link diagram
, characterized by the three rules: The pictures in the second rule represent brackets of the link diagrams which differ inside a disc as shown but are identical outside.