Luciano Melodia

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20182026

most citedPersistent Homology as Stopping-Criterion for Voronoi Interpolation

2 citations · 5 across the 10 of their papers we have counts for

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math.AT2026

Persistent Magnitude Homology for Quantitative Equational Theories

Luciano Melodia

A quantitative equational theory $U$ reasons about terms that agree up to a numerical error. It presents a free algebra $T_{U} A$ over a metric space $A$ of generators, the terms of t…

math.AT2026

Universal Coefficients and Mayer-Vietoris Sequence for Groupoid Homology

Luciano Melodia

We study homology of ample groupoids via the compactly supported Moore complex of the nerve. Let $A$ be a topological abelian group. For $n \geq 0$ set $C_n(\mathcal G;A) := C_c(\mat…

math.AT2026

Discrete Coefficients and Open Invariant Covers in the Homology of Ample Groupoids

Luciano Melodia

The homology of an ample groupoid is computed from the complex of compactly supported continuous functions on the nerve. Two hypotheses routinely imposed on this complex behave in…

math.AT2026

Groupoid Homology and Classifying-Space Homology Are Not Isomorphic

Luciano Melodia

For an ample groupoid $G$ , Matui-type groupoid homology $H_{∙} (G; Z)$ is built from the nerve $G_{∙}$ via the Moore complex of compact…

math.AT2024

Algebraic and Topological Persistence

Luciano Melodia

This thesis addresses the theory of topological spaces and the foundations of persistence theory. We will discuss chain complexes and the associated simplicial homology groups, as…