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arXiv · 2604.08166

L-fuzzy simplicial homology

Javier Perera-Lago·Alvaro Torras-Casas·Rocio Gonzalez-Diaz
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Abstract

Simplicial homology is a classical tool that assigns a sequence of modules to a simplicial complex, providing invariants for the study of its topological properties. In this article, we introduce the notion of L-fuzzy simplicial homology, a generalization of simplicial homology for L-fuzzy subcomplexes, in which each simplex is assigned a value from a completely distributive lattice L. We present its definition and main properties and describe methods to compute its structure. In addition, we interpret filtrations over a poset and chromatic datasets in this setting, opening a door to further applications in topological data analysis.

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Javier Perera-Lago, Alvaro Torras-Casas, Rocio Gonzalez-Diaz. 2026-04-09. L-fuzzy simplicial homology. https://arxiv.org/abs/2604.08166

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