Abstract For algebras of global dimension 2 arising from a cut of the quiver with potential associated with a triangulation of an unpunctured surface, Amiot-Grimeland defined integer-valued functions on the first homology groups of the surfaces. Derived equivalences translate to the existence of automorphisms of surfaces preserving these functions. We generalize this to punctured surfaces. Moreover, we show that all algebras of global dimension 2 arising from an arbitrarily punctured polygon are derived equivalent. We also combinatorially characterize the QPs of triangulations that do not admit cuts and those cuts that yield algebras of global dimension greater than 2.

中文翻译：

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全局维度 2 的曲面切割代数的派生不变量 II：穿孔案例

摘要 对于由具有与未穿孔表面的三角剖分相关联的势的箭袋切割产生的全局维度 2 代数，Amiot-Grimeland 在表面的第一个同调群上定义了整数值函数。导出的等价性转化为保留这些函数的表面自同构的存在。我们将其推广到穿孔表面。此外，我们证明了由任意穿孔多边形产生的全局维度 2 的所有代数都是等效的。我们还组合描述了不允许切割的三角剖分的 QP 和产生全局维度大于 2 的代数的那些切割。