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Artículo
Rectifications of A-Algebras
(2007)
In this article, in the setting of connected DG-modules, we prove that, for any A -algebra M mi i≥1 , there is a chain contraction from a DG-algebra AM onto the DG-module M such that the A -algebra structure induced ...
Artículo
Algebra Structures on the Comparison of the Reduced Bar Construction and the Reduced W-Construction
(Taylor and Francis, 2009)
For a simplicial augmented algebra K, Eilenberg–Mac Lane constructed a chain map . They proved that g is a reduction (homology isomorphism) and conjectured that it is also the injection of a contraction (special homotopy ...
Artículo
Homological spanning forest framework for 2D image analysis
(2012)
A 2D topology-based digital image processing framework is presented here. This framework consists of the computation of a flexible geometric graph-based structure, starting from a raster representation of a digital image ...
Artículo
Computing Adem Cohomology Operations
(Cornell University, 2006)
We deal with the problem of obtaining explicit simplicial formu- lae defining the classical Adem cohomology operations at the cochain level. Having these formulae at hand, we design an algorithm for com- puting these ...
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
Simplification techniques for maps in simplicial topology
(2005)
This paper offers an algorithmic solution to the problem of obtaining “economical” formulae for some maps in Simplicial Topology, having, in principle, a high computational cost in their evaluation. In particular, maps of ...
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
Membrane parallelism for discrete Morse theory applied to digital images
(2015)
In this paper, we propose a bio-inspired membrane computational framework for constructing discrete Morse complexes for binary digital images. Our approach is based on the discrete Morse theory and we work with cubical ...
Artículo
Parallel connected-Component-Labeling based on homotopy trees
(Elsevier, 2020)
Taking advantage of the topological and isotopic properties of binary digital images, we present here anew algorithm for connected component labeling (CLL). A local-to-global treatment of the topologicalinformation within ...
Artículo
On p-minimal homological models of twisted tensor products of elementary complexes localised over a prime
(American Mathematical Society, 1999)
In this paper, working over Z(p) and using algebra perturbation results from [18], p-minimal homological models of twisted tensor products (TTPs) of Cartan’s elementary complexes are obtained. Moreover, making use of the ...