A Sharp Curvature Threshold for GLMY Path Homology

Shuliang Bai, Jingyan Li, Shing-Tung Yau

Let $G$ be a finite simple graph with at least one edge. We prove the sharp vanishing theorem \[ κ_{\min}^{\mathrm{LLY}}(G)>\frac12 \quad\Longrightarrow\quad \PathH_1(G;\R)=0. \] E…