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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…
math.AT2024
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…
math.AT2024
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…