关于CAT（0）立方复形与旗形单纯复形
Relating CAT(0) cubical complexes and flag simplicial complexes
摘要：
给定一个有限的CAT（0）立方复形，我们定义一个与之相关的旗形单纯复形，称为交叉复形。我们表明，交叉复杂的原始立方复杂的组合信息：例如，在立方复杂的超平面对应于顶点链接的交叉复杂，和交叉复杂是平衡的，当且仅当立方复杂是立方平衡的。最有意义的结果是CAT（0）立方复形和旗形单纯复形的$f$ -向量集在可逆线性变换下是相等的。
英文摘要：
Given a finite CAT(0) cubical complex, we define a flag simplicial complex associated to it, called the crossing complex. We show that the crossing complex holds much of the combinatorial information of the original cubical complex: for example, hyperplanes in the cubical complex correspond to vertex links in the crossing complex, and the crossing complex is balanced if and only if the cubical complex is cubically balanced. The most significant result is that the sets of $f$-vectors of CAT(0) cubical complexes and flag simplicial complexes are equal, up to an invertible linear transformation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
