Evolutions of hypergraphs and their embedded homology

Hypergraphs are higher-dimensional generalizations of graphs. An (abstract) simplicial complex is a hypergraph such that all the faces of hyperedges are still hyperedges. The topology of a hypergraph can be investigated by its embedded homology, the homology of its associated complex, and the homology of its lower-associated complex. In this paper, we study the evolutions of hypergraphs as well as the induced homomorphisms of the embedded homology groups. The main result of this paper investigates the homomorphisms of the embedded homology induced from evolutions of hypergraphs and the relations with the lower-associated simplicial complexes.