Jones polynomial surgery invariant (${\tau }_r(M_L)={\mathcal{D}}^{-m}(p_{+}/\mathcal{D}{)}^{-\sigma (L)}⟨L(\Omega )⟩$)

For an m-component integral framed surgery link, normalize its full colored bracket by the displayed expression, where $\sigma (L)$ is the signature of its linking matrix. The Kirby color handle-slide identity handles slides; $p_{+}{p}_{-}={\mathcal{D}}^2$ cancels disjoint plus- or minus-one-framed unknots. Kirby calculus therefore makes this an oriented 3-manifold invariant. This convention has ${\tau }_r(S^3)=1$.

// Target: module-theory.bigb