8 papers
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…
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…
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…
A "Periodicity" Phenomenon of the Attaching Map of the Suspended Two-Cell Complex
Juxin Yang, Fengchun Lei, Jingyan Li +1
In this paper, we determine the 3-cell skeleton of , where is the homotopy fiber of the canonical pinch map from a suspension of a simply-connected 2-cell complex onto a sph…
IntComplex for high-order interactions
Xiang Liu, Ran Liu, Jingyan Li +2
Graphs serve as powerful tools for modeling pairwise interactions in diverse fields such as biology, material science, and social networks. However, they inherently overlook intera…
Primitive path homology
Jingyan Li, Yuri Muranov, Jie Wu +1
In this paper we introduce a primitive path homology theory on the category of simple digraphs. On the subcategory of asymmetric digraphs, this theory coincides with the path homol…
New Aspects of Analyzing Amyloid Fibrils
Xiaoxi Lin, Yunpeng Zi, Fengling Li +1
This is a summary of mathematical tools we used in research of analyzing the structure of proteins with amyloid form \cite{xi2024Top}. We defined several geometry indicators on the…
Homotopy Groups and Puppe Sequence of Digraphs
Jingyan Li, Jie Wu, Shing-Tung Yau +1
We introduce homotopy groups of digraphs that admit an intuitive description of grid structures, which is a variation of the GLMY homotopy groups introduced by Grigor'yan, Lin, Mur…