Unraveling chaos: A topological analysis of simplicial homology groups and their foldings

Abstract In this article, we introduce a new type of simplicial homology group called the chaotic simplicial homology group. We construct the structure of this group and obtain some types of conditional foldings and unfoldings restricted to the elements of the chaotic simplicial homology group. Also, we deduce the chaotic simplicial homology groups under the limit of foldings. We describe the variant and invariant of the chaotic simplicial homology group under the folding of a chaotic simplicial complex into itself. We use the chain of a commutative diagram on the simplicial complexes to induce the chain of a commutative diagram of simplicial homology groups.