有边Riemann surfaces和伴随多面体的变形
Deformations of bordered Riemann surfaces and associahedral polytopes
摘要：
本文研究了带边界点和标记点的加边Riemann曲面的模空间。这样的空间出现在开闭弦理论中，特别是关于具有拉格朗日子流形的全纯曲线。我们考虑一个组合框架，以查看紧化这个空间的基础上对裤子分解的表面，将其与众所周知的现象冒泡。我们的主要结果分类所有这样的空间，可以实现为凸多胞体。基于立方体的截断引入了一种新的多面体，其组合和代数结构与结合面体和多重面体的推广有关。
英文摘要：
We consider the moduli space of bordered Riemann surfaces with boundary and marked points. Such spaces appear in open-closed string theory, particularly with respect to holomorphic curves with Lagrangian submanifolds. We consider a combinatorial framework to view the compactification of this space based on the pair-of-pants decomposition of the surface, relating it to the well-known phenomenon of bubbling. Our main result classifies all such spaces that can be realized as convex polytopes. A new polytope is introduced based on truncations of cubes, and its combinatorial and algebraic structures are related to generalizations of associahedra and multiplihedra.
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