Primitive path homology

Jingyan Li; Yuri Muranov; Jie Wu; Shing-Tung Yau

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arXiv · 2411.18955

Primitive path homology

Jingyan Li·Yuri Muranov·Jie Wu·Shing-Tung Yau

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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 $a,b$ two different vertices of a digraph. 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.

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BibTeX RIS

Jingyan Li, Yuri Muranov, Jie Wu, Shing-Tung Yau. 2024-11-28. Primitive path homology. https://arxiv.org/abs/2411.18955

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