Preprint
Aug 2026
A Sharp Curvature Threshold for GLMY Path Homology
Let $G$ be a finite simple graph with at least one edge. We prove the sharp vanishing theorem \[ \kappa_{\min}^{\mathrm{LLY}}(G)>\frac12 \quad\Longrightarrow\quad \PathH_1(G;\R)=0. \] Equivalently, nonzero first GLMY path homology forces an edge of Lin--Lu--Yau curvature at most $1/2$. The threshold $1/2$ is sharp and...
Shu-Liang Bai, Jing-Yan Li, Shing-Tung Yau
· 0 citations