منابع مشابه
Computing Homology
The aim of the paper is to give a retrospective of authors’ research on homology computing in past six years. The discussed topics include cubical complexes, reduction algorithm for computing homology of finitely generated chain complexes, and an algorithmic construction of homology of continuous maps via multivalued acyclic representations. The motivation comes from computational dynamics but ...
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In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph theoretical operations. We use iterated Morse decomposition, which allows us to sidetrack many problems related to the standard discrete Morse theory. In particu...
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Let R be a commutative ring and I an ideal in R which is locally generated by a regular sequence of length d. Then, each f. g. projective R/I-module V has an Rprojective resolution P. of length d. In this paper, we compute the homology of the n-th Koszul complex associated with the homomorphism P1 → P0 for all n ≥ 1, if d = 1. This computation yields a new proof of the classical Adams-Riemann-R...
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The Koszul homology of modules of the polynomial ring R is a central object in commutative algebra. It is strongly related with the minimal free resolution of these modules, and thus with regularity, Hilbert functions, etc. Here we consider the case of modules of the form R/I where I is a monomial ideal. So far, some good algorithms have been given in the literature and implemented in different...
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This report provides theoretical justification for the use of discrete Morse theory for the computation of homology and persistent homology, an overview of the state of the art for the computation of discrete Morse matchings and motivation for an interest in these computations, particularly from the point of view of topological data analysis. Additionally, a new simulated annealing based method...
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ژورنال
عنوان ژورنال: Homology, Homotopy and Applications
سال: 2003
ISSN: 1532-0073,1532-0081
DOI: 10.4310/hha.2003.v5.n2.a8