Representing Topological Structures Using Cell-Chains

A new topological representation of surfaces in higher dimensions, “cell-chains” is developed. The representation is a generalization of Brisson’s cell-tuple data structure. Cell-chains are identical to cell-tuples when there are no degeneracies: cells or simplices with identified vertices. The proof of correctness is based on axioms true for maps, such as those in Brisson’s cell-tuple representation. A critical new condition (axiom) is added to those of Lienhardt’s n-G-maps to give “cell-maps”. We show that cell-maps and cell-chains characterize the same topological representations.