Incremental Computation of the Homology of Generalized Maps: An Application of Effective Homology Results

This paper deals with the incremental computation of the homology of " cellular " combinatorial structures, namely combinatorial maps and incidence graphs. " Incremental " is related to the operations which are applied to construct such structures: basic operations, i.e. the creation of cells and the identification of cells, are considered in the paper. Such incremental computation is done by applying results of effective homology [RS06]: a correspondence between the chain complex associated with a given combinatorial structure is maintained with a " smaller " chain complex , from which the homology groups and homology generators can be more efficiently computed.