报告题目：A Discrete Morse Theory for Hypergraphs

报 告 人：任世全(清华大学)

报告时间：2020.1.5 11:00-11:30

报告地点：数学中心 学术报告厅 （至善楼 234）

主 持 人：吴杰

摘 要：

A hypergraph can be obtained from a simplicial complex by deleting some non-maximal simplices. By [1], a hypergraph gives an associated simplicial complex. By [2], the embedded homology of a hypergraph is the homology of the infimum chain complex, or equivalently, the homology of the supremum chain complex. In this paper, we generalize the discrete Morse theory for simplicial complexes by R. Forman [3–5] and give a discrete Morse theory for hypergraphs. We use the critical simplices of the associated simplicial complex to construct a sub-chain complex of the infimum chain complex and a sub-chain complex of the supremum chain complex, then prove that the embedded homology of a hypergraph is isomorphic to the homology of the constructed chain complexes. Moreover, we define discrete Morse functions on hypergraphs and compute the embedded homology in terms of the critical hyperedges. As by-products, we derive some Morse inequalities and collapse results for hypergraphs.