2021/04/03 by Shiquan Ren, Ren, Shiquan
Computer Science · Mathematics · #08A50 #55U15 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 55U10 #Secondary 53A45 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2104.01452
openalex publication_date 2021/04/03 · openalex created_date 2021/08/02 · openalex updated_date 2026/07/28
Let V be a finite set. Let K be a simplicial complex with its vertices in V. In this paper, we discuss some differential calculus on V. We construct some constrained homology groups of K by using the differential calculus on V. Moreover, we define an independent hypergraph to be the complement of a simplicial complex in the complete hypergraph on V. Let L be an independent hypergraph with its vertices in V. We construct some constrained cohomology groups of L by using the differential calculus on V.