Presentation conjecture for the skein algebra of a surface

Let $\Sigma$ be the surface under consideration, let $\bar{\Gamma}(\Sigma)$ be the extended mapping class group, and let $\mathcal{A}(\Gamma(\Sigma))$ be the quotient algebra defined from a presentation of $\bar{\Gamma}(\Sigma)$ and its action on the skein algebra. The skein algebra is denoted by $\mathcal{S}(\Sigma,\mathbb{Q}(A))$. Presentation conjecture. There exists a presentation of $\bar{\Gamma}(\Sigma)$ for which

$$\mathcal{A}(\Gamma(\Sigma))\cong\mathcal{S}(\Sigma,\mathbb{Q}(A))$$

as noncommutative $\mathbb{Q}(A)$-algebras. The preceding corollary gives a canonical surjection from $\mathcal{A}(\Gamma(\Sigma))$ onto the skein algebra; the conjecture asserts that a suitable presentation makes this surjection an isomorphism.