Work

Primitive path homology

Year: 2025

Type: article

Abstract: In this paper we introduce a primitive path homology theory in the category of simple digraphs.In the subcategory of asymmetric digraphs, this theory coincides with the path homology theory introduced by Grigor'yan, Lin, Muranov and Yau, but these theories differ in the general case.We study properties of the primitive path homology and describe relations between the primitive path homology and the path homology.Our approach gives a possibility to construct primitive homology theories of paths which have a given tail vertex a or (and) a given head vertex b.We study these theories and describe also relationships between them and the path homology theory.

Source: Data Analytics and Topology

DOI: 10.4310/daat.250513005500

Authors: Jingyan Li, Yuri Muranov, Jie Wu, Shing-Tung Yau

Institutions: Beijing Institute of Mathematical Sciences and Applications, University of Warmia and Mazury in Olsztyn, Tsinghua University

Language: English

Topic: Topological and Geometric Data Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

OpenAlex ID: W4411333151

FWCI:

Cites: 10

Cited by:

Related to: 10