ScalingStacks

Proposition 9 For an oriented link $L,$

$$K(L)=(1-q^{2})\sum_{i\in\mathbb{Z}}(-1)^{i}\widehat{\chi}(H^{i}(D))$$

(47)

where $K(L)$ is the scaled Kauffman bracket, defined in Section 2.4, $\widehat{\chi}$ is the Euler characteristic (see Section 2.1) and $D$ is any diagram of $L.$