Teichmüller理论的三维Calabi-Yau范畴
3-d Calabi--Yau categories for Teichmüller theory
摘要：
对于$g,n\geq 0$，构造了一个三维Calabi-Yau $A_\infty$范畴$\mathcal C_{g,n}$，使得Bridgeland稳定性条件空间的一个分支$\mathrm{Stab}(\mathcal C_{g,n})$是亏格$g$曲面上的二次微分的模空间，该曲面具有单零点和$n$单极点.对于模空间中的一个泛点，相应的量子/精化Donaldson-Thomas不变量是根据平面上由二次微分确定的有限长测地线的计数来计算的.因此，这些计数满足跨壁公式。
英文摘要：
For $g,n\geq 0$ a 3-dimensional Calabi-Yau $A_\infty$-category $\mathcal C_{g,n}$ is constructed such that a component of the space of Bridgeland stability conditions, $\mathrm{Stab}(\mathcal C_{g,n})$, is a moduli space of quadratic differentials on a genus $g$ surface with simple zeros and $n$ simple poles. For a generic point in the moduli space the corresponding quantum/refined Donaldson--Thomas invariants are computed in terms of counts of finite-length geodesics on the flat surface determined by the quadratic differential. As a consequence, these counts satisfy wall-crossing formulas.
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