Abstract
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.
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Partially supported by the Polish Committee for Scientific Research (KBN), grant no. 2 P03A 041 24, Polish MNSzW, Grant N201 037 31/3151 and Polish MNSzW, Grant N N201 419639.
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Mrozek, M. Čech Type Approach to Computing Homology of Maps. Discrete Comput Geom 44, 546–576 (2010). https://doi.org/10.1007/s00454-010-9255-2
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DOI: https://doi.org/10.1007/s00454-010-9255-2