9 papers
Homological critical points for hypergraphs and simplicial complexes
Shiquan Ren
In this paper, we study the homological critical points for persistence hypergraphs and persistence simplicial complexes. With the help of the relative homology groups, we define t…
Hypergraphs on Riemannian manifolds and their double homology
Shiquan Ren
In this paper, by constructing double homology for graded submanifolds of -manifolds, we study the double homology of hyper(di)graphs on Riemannian manifolds. With the help of t…
Homological obstructions for regular embeddings of graphs
Shiquan Ren
In [36, Section 8], the present author proposed the hypergraph obstruction for the existence of k-regular embeddings. In this paper, we develop the hypergraph obstruction concretel…
Topological persistence of configuration spaces and independence complexes for digraphs
Shiquan Ren
We study the topological persistence of the (path) configuration spaces and the (path) independence complexes for digraphs as well as their underlying graphs. We construct some can…
Persistent bundles over configuration spaces and obstructions for regular embeddings
Shiquan Ren
We construct persistent bundles over configuration spaces of hard spheres and use the characteristic classes of these persistent bundles to give obstructions for embedding problems…
Double complexes for configuration spaces and hypergraphs on manifolds
Shiquan Ren
In this paper, we consider hypergraphs whose vertices are distinct points moving smoothly on a Riemannian manifold M. We take these hypergraphs as graded submanifolds of configurat…
Differential Calculus on Hypergraphs and Mayer-Vietoris Sequences for the Constrained Persistent Homology
Shiquan Ren
In this paper, we study the discrete differential calculus on hypergraphs by using the Kouzul complexes. We define the constrained (co)homology for hypergraphs and give the corresp…
Differential calculus for free algebra and constrained homology
Shiquan Ren
In [Discrete differential calculus on simplicial complexes and constrained homology, Chin. Ann. Math. Ser. B 44(4), 615-640, 2023], the constrained (co)homology for simplicial comp…
Discrete Differential Calculus on Simplicial Complexes and Constrained Homology
Shiquan Ren
Let be a finite set. Let be a simplicial complex with its vertices in . In this paper, we discuss some differential calculus on . We construct some constrai…