局部温和代数的不相交复形与非交叉复形
Non-kissing and non-crossing complexes for locally gentle algebras
AI总结：
本文从局部温和有界箭图构造不相交复形，并利用带标记穿孔曲面的对偶剖分定义手风琴复形与障碍滑雪复形，证明三者同构且为纯薄复形，其面间有τ-倾斜型突变，并给出箭图与曲面间的双射。
摘要：
从一个局部温和的有界箭图出发，我们一方面定义了一个单纯复形，称为不相交复形。另一方面，我们构造了一个带边界、带标记、带穿孔的有向曲面，并赋予其一对对偶剖分。从这些几何数据出发，我们定义了两个单纯复形：手风琴复形和障碍滑雪复形，这推广了A. Garver和T. McConville在圆盘情形下的工作。我们证明了这三个单纯复形是同构的，并且它们是纯的且薄的。特别地，它们的面之间存在类似于τ-倾斜突变的概念。在此过程中，我们还构造了局部温和有界箭图的同构类集合与带边界、带标记、带穿孔的有向曲面（赋予一对对偶剖分）的同胚类集合之间的互逆双射。
英文摘要：
Starting from a locally gentle bound quiver, we define on the one hand a simplicial complex, called the non-kissing complex. On the other hand, we construct a punctured, marked, oriented surface with boundary, endowed with a pair of dual dissections. From those geometric data, we define two simplicial complexes: the accordion complex, and the slalom complex, generalizing work of A. Garver and T. McConville in the case of a disk. We show that all three simplicial complexes are isomorphic, and that they are pure and thin. In particular, there is a notion of mutation on their facets, akin to $τ$-tilting mutation. Along the way, we also construct inverse bijections between the set of isomorphism classes of locally gentle bound quivers and the set of homeomorphism classes of punctured, marked, oriented surfaces with boundary, endowed with a pair of dual dissections.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
