论文标题
分级装饰的标记表面：calabi-yau-$ \ m athbb {x} $柔和代数类别
Graded decorated marked surfaces: Calabi-Yau-$\mathbb{X}$ categories of gentle algebras
论文作者
论文摘要
令$ \ mathbf {s} $为标记的表面。我们构建了Calabi-yau的字符串模型-U \ Mathbb {X} $ category $ \ Mathcal {d} _ \ Mathbb {X}（\ Mathbf {s} _ \ bigtriangleup）$，通过年体的dms（=装饰的表面）$ \ mathbf {s}。我们证明了$ \ mathbf {s} _ \ bigtriangleup $的编织扭曲组与$ \ Mathcal {d} _ \ Mathbb {x}（\ MathBf {s} _ \ bigtriangleup）$的球形扭曲组之间的同构型组。我们还给出了Lagrangian Immersion $ \ Mathcal {d} _ \ infty（\ Mathbf {s}）\ to \ Mathcal {D} _ \ Mathbb {X}（\ Mathbf {s} _ \ bigtriangleup）$的拓扑实现。 $ \ MATHCAL {D} _ \ infty（\ MathBf {s}）$是与$ \ Mathbf {S} $相关的拓扑福卡亚类别，这是三角形，等于某些分级柔和的代数的有限类别。这概括了[Qiu，Qiu-Zhou]在Calabi-yau-3情况下的先前作品，并且还统一了Calabi-yau-$ \ infty $ case $ \ case $ \ Mathcal {d} _ \ infty（\ Mathbf {s}）
Let $\mathbf{S}$ be a graded marked surface. We construct a string model for Calabi-Yau-$\mathbb{X}$ category $\mathcal{D}_\mathbb{X}(\mathbf{S}_\bigtriangleup)$, via the graded DMS (=decorated marked surface) $\mathbf{S}_Δ$. We prove an isomorphism between the braid twist group of $\mathbf{S}_\bigtriangleup$ and the spherical twist group of $\mathcal{D}_\mathbb{X}(\mathbf{S}_\bigtriangleup)$, and $\mathbf{q}$-intersection formulas. We also give a topological realization of the Lagrangian immersion $\mathcal{D}_\infty(\mathbf{S})\to\mathcal{D}_\mathbb{X}(\mathbf{S}_\bigtriangleup)$, where $\mathcal{D}_\infty(\mathbf{S})$ is the topological Fukaya category associated to $\mathbf{S}$, that is triangle equivalent to the bounded derived category of some graded gentle algebra. This generalizes previous works of [Qiu, Qiu-Zhou] in the Calabi-Yau-3 case and and also unifies the Calabi-Yau-$\infty$ case $\mathcal{D}_\infty(\mathbf{S})$ (cf. [Haiden-Katzarkov-Kontsevich, Opper-Plamondon-Schroll]).
