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Artículo
Homological optimality in Discrete Morse Theory through chain homotopies
(2012)
Morse theory is a fundamental tool for analyzing the geometry and topology of smooth manifolds. This tool was translated by Forman to discrete structures such as cell complexes, by using discrete Morse functions or ...
Artículo
Computation of cubical homology, cohomology, and (co)homological operations via chain contraction
(2015)
We introduce algorithms for the computation of homology, cohomology, and related operations on cubical cell complexes, using the technique based on a chain contraction from the original chain complex to a reduced one that ...
Artículo
Making Sullivan Algebras Minimal Through Chain Contractions
(Springer, 2021)
In this note, we provide an algorithm that, starting with a Sullivan algebra gives us its minimal model. More concretely, taking as input a (nonminimal) Sullivan algebra A with an ordered finite set of generators preserving ...
Artículo
Searching combinatorial optimality using graph-based homology information
(2015)
This paper analyses the topological information of a digital object O under a combined combinatorial-algebraic point of view. Working with a topology-preserving cellularization K(O) of the object, algebraic and combinatorial ...
Artículo
An algorithm to compute minimal Sullivan algebras
(Cornell University, 2019)
In this note, we give an algorithm that starting with a Sullivan algebra gives us its minimal model. This algorithm is a kind of modified AT-model algorithm used to compute in the past other kinds of topology information such ...