The Cohomology of the Vietoris-Rips Complex of a Hypercube Graph

All of the nouns in the title will be defined. The Vietoris-Rips complex of a hypercube graph is a natural object that arises in coding theory. There are two integer parameters: n – the size of the hypercube and r- the scaling distance. There are recent results by Adams et-al describing their topology.
For example, the Vietoris-Rips complex for the n-dimensional hypercube at scale 2 is a wedge (bouquet) of 3 dimensional spheres. The methods used are geometric. I will describe an algebraic approach for computing the cohomology of the Vietoris-Rips complex.