Cech Type Approach to Computing Homology of Maps
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.