论文标题
复曲面拓扑中的矩阵
Matroids in toric topology
论文作者
论文摘要
在本文中，我们研究了从组合的角度孤立的固定点的歧管上的一般圆环动作。研究的主要对象是此类作用的面部子曼叶的poset。我们介绍了局部几何poset的概念 - 以几何晶格为局部建模的分级POSET，并证明对于任何圆环动作，其脸部的poset在本地几何上。接下来，我们讨论面孔和GKM理论之间的关系。特别是，我们定义了抽象的GKM图纸的面部底漆，并展示了如何从其GKM-Graph中重建歧管的脸部poset。
In this paper we study general torus actions on manifolds with isolated fixed points from combinatorial point of view. The main object of study is the poset of face submanifolds of such actions. We introduce the notion of a locally geometric poset -- the graded poset locally modelled by geometric lattices, and prove that for any torus action, the poset of its faces is locally geometric. Next we discuss the relations between posets of faces and GKM-theory. In particular, we define the face poset of an abstract GKM-graph and show how to reconstruct the face poset of a manifold from its GKM-graph.
