论文标题
骨骼补充的拓扑
Topology of complements of skeletons
论文作者
论文摘要
考虑到多面体复杂$ x $，我们检查了其$ k $ skeleton的拓扑补充。我们构建了一个长期的精确序列，该序列将骨骼补充的同源物和$ x $中的面孔的链接构建，并使用这个长长的精确序列，我们获得了Cohen-Macaulay和Leray Complextes的特征，堆叠球，以及以其骨骼补充的方式获得邻居球。我们还将这些结果应用于CAT（0）立方体复合物，并在这样的复合物和相关的简单复合物，即交叉复合物之间找到新的相似性。
Given a polytopal complex $X$, we examine the topological complement of its $k$-skeleton. We construct a long exact sequence relating the homologies of the skeleton complements and links of faces in $X$, and using this long exact sequence, we obtain characterisations of Cohen-Macaulay and Leray complexes, stacked balls, and neighbourly spheres in terms of their skeleton complements. We also apply these results to CAT(0) cubical complexes, and find new similarities between such a complex and an associated simplicial complex, the crossing complex.
