4 problems

Let $S$ be a surface with holes, let $S'$ be obtained by cutting $S$ along a simple loop, and let $\gamma_\pm$ be the two new boundary components. Let ${\bf V}_{G,S;\lambda}$ be th…

Let $G=\operatorname{PGL}_{n+1}$, let $S$ be a marked surface, and let $c$ be an essential simple closed curve on $S$. Let $S'$ be obtained by cutting $S$ open along $c$, and let…

Tensor-product equivalence conjecture. The map above induces an equivalence of monoidal categories

Let $\mathfrak{S} = \Sigma \setminus \mathcal{P}$ be a triangulable marked surface, let $\Delta$ be an ideal triangulation, and let $\hbar \in \mathbb{R}_{>0}$. For an essential si…