Cech Type Approach to Computing Homology of Maps

Cech Type Approach to Computing Homology of Maps,10.1007/s00454-010-9255-2,Discrete & Computational Geometry,Marian Mrozek

Cech Type Approach to Computing Homology of Maps   (Citations: 3)
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A new approach to algorithmic computation of the homology of spaces and maps is presented. The key point of the approach is a change in the representation of sets. The proposed representation is based on a combinatorial variant of the Čech homology and the Nerve Theorem. In many situations, this change of the representation of the input may help in bypassing the problems with the complexity of the standard homology algorithms by reducing the size of necessary input. We show that the approach is particularly advantageous in the case of homology map algorithms.
Journal: Discrete & Computational Geometry - DCG , vol. 44, no. 3, pp. 546-576, 2010
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    • ...Another approach to computing homology of maps presented in [23] better utilizing the outcome of numerical algorithms for Poincar´e maps in dierential equations, is under development...

    Tomasz KaczynskiIet al. Computing homology

    • ...Similarly, in the context of computing the homology of maps it has been shown in [18] that the restriction to uniform cubical grids leads to inefficiencies which in principle can be addressed by representing the objects of interest in a less stringent way...

    Paweł Dłotkoet al. Coreduction Homology Algorithm for Regular CW-Complexes

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