论文标题
图形如何不像流形？
How is a graph not like a manifold?
论文作者
论文摘要
对于平滑的歧管$ x $，带有隔离固定点的紧凑型圆环$ t $的等效正式动作，我们调查了面部submanifolds的分级poset $ s（x）$的全球同源性属性。我们证明，在每个固定点上，切线权重的$ j $独立的条件意味着$（J+1）$ - skeleta $ s（x）_r $ for $ r> j+1 $的acemclicity。该结果为GKM图提供了必要的拓扑条件，使其成为某些GKM歧管的GKM图。我们使用特定的环体论证来描述dimension $ 2N $的均等形式形式的同类同胞代数，并在其GKM图上的某些可着色性假设下，$（n-1）$ - $（n-1）$（n-1）$尺寸的独立动作。此描述将模棱两可的同一个同学代数与简单poset的面部代数相关联。这种观察结果强调了复杂性的动作与圆环歧管之间的某些相似性。
For an equivariantly formal action of a compact torus $T$ on a smooth manifold $X$ with isolated fixed points we investigate the global homological properties of the graded poset $S(X)$ of face submanifolds. We prove that the condition of $j$-independency of tangent weights at each fixed point implies $(j+1)$-acyclicity of the skeleta $S(X)_r$ for $r>j+1$. This result provides a necessary topological condition for a GKM graph to be a GKM graph of some GKM manifold. We use particular acyclicity arguments to describe the equivariant cohomology algebra of an equivariantly formal manifold of dimension $2n$ with an $(n-1)$-independent action of $(n-1)$-dimensional torus, under certain colorability assumptions on its GKM graph. This description relates the equivariant cohomology algebra to the face algebra of a simplicial poset. Such observation underlines certain similarity between actions of complexity one and torus manifolds.
