3 citations · 4 across the 8 of their papers we have counts for
8 papers
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…
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…
On Bredon's trick: from local to global properties
Mauricio Angel
One of the most interesting problems that arise when studying certain structures on topological spaces and in particular on differential manifolds, is to be able to extend the prop…
-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…
On the (3,N) Maurer-Cartan equation
Mauricio Angel, Jaime Camacaro, Rafael Diaz
Deformations of the 3-differential of 3-differential graded algebras are controlled by the (3,N) Maurer-Cartan equation. We find explicit formulae for the coefficients appearing in…
On the -analogue of the Maurer-Cartan equation
Mauricio Angel, Rafael Díaz
We consider deformations of the differential of a -differential graded algebra. We prove that it is controlled by a generalized Maurer-Cartan equation. We find explicit formulae…
N-flat connections
Mauricio Angel, Rafael Díaz
We construct geometric examples of N-differential graded algebras such as the algebra of differential forms of depth on an affine manifold, and -flat covariant derivatives.
On -differential graded algebras
Mauricio Angel, Rafael Díaz
We introduce the concept of -differential graded algebras (N-dga), and study the moduli space of deformations of the differential of a N-dga. We prove that it is controlled by w…