4 papers
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…