Removal and Contraction Operations in nD Generalized Maps for Efficient Homology Computation

In this paper, we show that contraction operations preserve the homology of nD generalized maps, under some conditions. This result extends the similar one given for removal operations in [6]. Removal and contraction operations are used to propose an efficient algorithm that compute homology generators of nD generalized maps. Its principle consists in simplifying a generalized map as much as possible by using removal and contraction operations. We obtain a generalized map having the same homology than the initial one, while the number of cells decreased significantly.