4 papers
Cohomological properties of the Vietoris--Rips Complex of a Hypercube Graph
Martin Bendersky, Salvatore Elia, Jelena Grbic
We develop a toric topological framework for studying the cohomology of Vietoris--Rips complexes of hypercube graphs. Using total domination invariants and spectral met…
-Bad Spheres
Martin Bendersky, Robert Thompson
In this paper we look at the -completion of topological spaces where is a -local ring spectrum. After a brief review of the concept of -completion, we specialize to th…
A Spectral Sequence for a Graded Linear Map
Larry Bates, Martin Bendersky, Richard Churchill
We apply the method of spectral sequences to study classical problems in analysis. We illustrate the method by finding polynomial vector fields that commute with a given polynomial…
On the Connectivity of the Vietoris-Rips Complex of a Hypercube Graph
Martin Bendersky, Jelena Grbic
We bring in the techniques of independence complexes and the notion of total dominating sets of a graph to bear on the question of the connectivity of the Vietoris-Rips complexes $…