通过离散莫尔斯理论计算图的2粒子无序构形空间的Borel-Moore同调
Borel-Moore Homology of 2-Particle Unordered Configuration Spaces of Graphs via Discrete Morse Theory
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中文总结 AI 辅助
本研究通过离散莫尔斯理论定义图的2粒子无序构形空间的开正则胞腔复形上的莫尔斯函数，借助同构关系得出其Borel-Moore同调群由图的第一贝蒂数决定的结论。
中文摘要 AI 辅助
我们在源于图Γ的2粒子无序构形空间的开正则胞腔复形C₂(Γ)上定义了一个离散莫尔斯函数，计算了关联莫尔斯复形的同调。利用Knudson与Scoville建立的C₂(Γ)的Borel-Moore同调与莫尔斯复形同调间的同构，我们得出结论：C₂(Γ)的Borel-Moore同调群完全由Γ的第一贝蒂数决定。
英文摘要
We define a discrete Morse function on the open regular cell complex $C_2(Γ)$, arising from the $2$-particle unordered configuration space of a graph $Γ$. We compute the homology of the associated Morse complex. Using an isomorphism established by Knudson and Scoville between the Borel-Moore homology of $C_2(Γ)$ and the homology of the Morse complex, we conclude that the Borel-Moore homology groups of $C_2(Γ)$ are completely determined by the first Betti number of $Γ$.
