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math.AT2026
Signed GLMY Homology of Signed Graphs via Double Covers
Shuliang Bai, Jingyan Li, Shing-Tung Yau
We define a signed GLMY chain complex over for signed digraphs using sheet-labelled regular paths. The complex is naturally isomorphic to the deck anti-invariant subco…
math.AT2026
A Sharp Curvature Threshold for GLMY Path Homology
Shuliang Bai, Jingyan Li, Shing-Tung Yau
Let 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…
math.AT2026
Persistent magnitude homology on finite metric space
Wanying Bi, Hongsong Feng, Jingyan Li +1
Magnitude homology is an emerging approach that captures the intrinsic topological and geometric features of metric spaces. It offers a distinct theoretical lens for interpreting s…