弧复形的结构与奇性
The Structure and Singularities of Arc Complexes
摘要：
一个经典的组合事实是：由凸平面多边形中不相交嵌入的弦组成的单纯复形是一个球面。对于任何非空边界曲面F，存在一个类似的复弧（F），它由F中合适的等价弧类连接其边界分量组成。本文的主要结果是确定了弧复形Arc（F）也是球面的。这种分类的后果黎曼的模空间通过其已知的标识与类似的弧复杂的穿孔的情况下，没有边界。也就是说，可以描述自然细胞紧致化的本质特征。
英文摘要：
A classical combinatorial fact is that the simplicial complex consisting of disjointly embedded chords in a convex planar polygon is a sphere. For any surface F with non-empty boundary, there is an analogous complex Arc(F) consisting of suitable equivalence classes of arcs in F connecting its boundary components. The main result of this paper is the determination of those arc complexes Arc(F) that are also spherical. This classification has consequences for Riemann's moduli space via its known identification with an analogous arc complex in the punctured case with no boundary. Namely, the essential singulities of the natural cellular compactification can be described.
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。
