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math.AT2026
Deformations, Derived Categories, and Multiparameter Persistence: A Theoretical Framework
Mauricio Angel
Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic compl…
math.AT2026
Operational Calculus on Curved Differentials: Optimal N-Complex Bounds and Persistent Homology
Mauricio Angel
We establish a canonical normal form for the iterates of a curved differential in curved differential algebras (CDA). This operator calculus clarifies the underlying algebraic stru…
math.AT2011
-Analog Singular Homology of Convex Spaces
Mauricio Angel, Gabriel Padilla
In this article we study some interesting properties of the -Analog singular homology, which is a generalization of the usual singular homology, suitably adapted to the context…