L-fuzzy simplicial homology
Algebraic Topology
2026-04-10 v1
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.
Cite
@article{arxiv.2604.08166,
title = {L-fuzzy simplicial homology},
author = {Javier Perera-Lago and Alvaro Torras-Casas and Rocio Gonzalez-Diaz},
journal= {arXiv preprint arXiv:2604.08166},
year = {2026}
}