$q$-Stability conditions via $q$-quadratic differentials for Calabi-Yau-$\mathbb{X}$ categories

Akishi Ikeda, Yu Qiu

Categorically, we introduce the Calabi-Yau-$\mathbb{X}$ categories ${\mathcal{D}}_{\mathbb{X}}$ of a graded marked surface ${\mathbf{S}}^{\lambda }$, as a $q$-deformation of the topological Fuk…