ScalingStacks

Definition 4.2. Let $B$ be an oriented $3$-manifold diffeomorphic to ${\mathbb{R}}^{3}$. We define

$$M(B)\stackrel{{\scriptstyle\mathrm{def}}}{{=}}\{\textrm{diffeomorphisms }\phi\colon B\to{\mathbb{R}}^{3}\}.$$

Given an embedded link $L\subset B$, we define the subspace

$$M(B,L)\stackrel{{\scriptstyle\mathrm{def}}}{{=}}\{\phi\in M(B)|\phi(L)\text{ is }z\text{-generic and blackboard-framed}\},$$

and consider the bundle $\pi\colon T(B,L)\to M(B,L)$ of bigraded abelian groups, whose fiber at the point $\phi$ is $\mathrm{KhR}_{N}(\phi(L))$.