ScalingStacks

Definition 4.12. Let $L\subset S$ be a link embedded in a 3-sphere. Then we define the Khovanov–Rozansky homology of $L$ in $S$ to be

$$\mathrm{KhR}_{N}(S,L)\stackrel{{\scriptstyle\mathrm{def}}}{{=}}\Gamma_{\textrm{flat}}(T(S,L)),$$

the bigraded abelian group of flat sections of the bundle $T(S,L)$.