3 papers
math.AT2026
Magnitude Homology Is the Associated Graded of the Length Filtration
Luciano Melodia
Magnitude homology is graded by length and knows nothing of persistence. Its persistent refinement knows nothing of where its bars begin and end. We show that the two are one const…
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 be a topological abelian group. For set $C_n(\mathcal G;A) := C_c(\mat…
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…