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

Sylvie Alayrangues (1) , Laurent Fuchs (1) , Pascal Lienhardt (1) , Samuel Peltier (1)

1 XLIM-SIC - SIC

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.

Mots clés: combinatorial maps; effective homology

Domaines: Géométrie algorithmique [cs.CG]

Sylvie Alayrangues, Laurent Fuchs, Pascal Lienhardt, Samuel Peltier. Incremental Computation of the Homology of Generalized Maps: An Application of Effective Homology Results. 2015. ⟨hal-01142760v2⟩