Torus graphs and simplicial posets
Torus graphs and simplicial posets
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DOI：
10.1016/j.aim.2006.10.011
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发表时间：
2005-11
影响因子：
1.7
通讯作者：
H. Maeda;M. Masuda;T. Panov
中科院分区：
文献类型：
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作者：
H. Maeda;M. Masuda;T. Panov
对于几类重要的由环面作用的流形，关于作用的信息可以通过一个在其边上带有向量标签的正则n价图组合编码，我们称之为环面图。通过与GKM-图的类比，我们引入了环面图的等变上同调的概念，并证明了环面图同构于相应单纯偏序集的面环。这推广了以前关于环面流形的等变上同调的一系列结果。作为组合论的一个重要应用，我们证明了单纯偏序集是Cohen-Macaulay的，如果它的面环是Cohen-Macaulay。这就完成了Stanley提出的Cohen-Macaulay偏序集的代数刻画。我们还从代数和拓扑的角度研究了环面图和流形的爆破。
For several important classes of manifolds acted on by the torus, the information about the action can be encoded combinatorially by a regular n-valent graph with vector labels on its edges, which we refer to as the torus graph. By analogy with the GKM-graphs, we introduce the notion of equivariant cohomology of a torus graph, and show that it is isomorphic to the face ring of the associated simplicial poset. This extends a series of previous results on the equivariant cohomology of torus manifolds. As a primary combinatorial application, we show that a simplicial poset is Cohen–Macaulay if its face ring is Cohen–Macaulay. This completes the algebraic characterisation of Cohen–Macaulay posets initiated by Stanley. We also study blow-ups of torus graphs and manifolds from both the algebraic and the topological points of view.