Primitive path homology
Algebraic Topology
2024-12-02 v1
Abstract
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 homology theory which was introduced by Grigor'yan, Lin, Muranov, and Yau, but these theories are different in general case. We study properties of the primitive path homology and describe relations between the primitive path homology and the path homology. Let two different vertices of a digraph. Our approach gives a possibility to construct primitive homology theories of paths which have a given tail vertex or (and) a given head vertex . We study these theories and describe also relationships between them and the path homology theory.
Cite
@article{arxiv.2411.18955,
title = {Primitive path homology},
author = {Jingyan Li and Yuri Muranov and Jie Wu and Shing-Tung Yau},
journal= {arXiv preprint arXiv:2411.18955},
year = {2024}
}