AI 中文总结
本文针对有限中心实超平面排列的顶图，改进Koizumi的模长同调结果，利用典范上同调基确定其交叉分次模长上同调环，明确了直和项的秩性质。
AI 中文摘要
设$\boldsymbol{\textit{A}}$为有限中心实超平面排列，$\boldsymbol{\textit{G(A)}}$为其顶图。Koizumi近期证明了$\boldsymbol{\textit{G(A)}}$的交叉分次模长同调是无挠的，且由面标志自由索引。我们改进该结果，证明固定交叉向量和终端室确定一个秩至多为1的直和项。在$\boldsymbol{\textit{F}_2}$上，我们利用典范上同调基确定$\boldsymbol{\textit{G(A)}}$的交叉分次模长上同调环。
英文摘要
Let $\mathcal{A}$ be a finite central real hyperplane arrangement and let $\mathcal{G}(\mathcal{A})$ be its tope graph. Koizumi recently proved that the crossing-graded magnitude homology of $\mathcal{G}(\mathcal{A})$ is torsion-free and is freely indexed by face flags. We refine his result by proving that a fixed crossing vector and terminal chamber determine a summand of rank at most one. Over $\mathbb{F}_2$, we use the canonical cohomology basis to determine the crossing-graded magnitude cohomology ring of $\mathcal{G}(\mathcal{A})$.
Comments26 pages, 1 figure
