Finiteness conjecture for Kauffman bracket skein modules of manifolds with boundary

Let $\mathcal{R}$ be a ring containing an invertible element $A$, and let $\mathcal{S}(M,\mathcal{R})$ denote the Kauffman bracket skein module of a 3-manifold $M$. Throughout, write $\mathcal{S}(M)=\mathcal{S}(M,\mathbb{Q}(A))$. For a compact oriented 3-manifold $M$, let $\mathcal{S}(\partial M,\mathbb{Q}(A))$ act on $\mathcal{S}(M)$ by boundary gluing.

Finiteness conjecture. Let $M$ be a compact oriented 3-manifold. Then $\mathcal{S}(M)$ is a finitely generated $\mathcal{S}(\partial M, \mathbb{Q}(A))$-module.

The conjecture extends the known finite-dimensionality result for closed 3-manifolds to manifolds with boundary. The paper establishes it for the stated family of Seifert fibered spaces, while the general case remains open.