Definition
The bracket polynomial of any (unoriented) link diagram L, denoted <L>, is a polynomial in the variable, characterized by the three rules:
= 1, where O is the standard diagram of the unknot
The pictures in the second rule represent brackets of the link diagrams which differ inside a disc as shown but are identical outside. The third rule means that adding a circle disjoint from the rest of the diagram multiplies the bracket of the remaining diagram by -A2 - A-2.
Read more about this topic: Bracket Polynomial
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