Kunneth Theorems for Vietoris-Rips Homology

Abstract

We prove a Kunneth theorem for the Vietoris-Rips homology and cohomology of a semi-uniform space. We then interpret this result for graphs, where we show that the Kunneth theorem holds for graphs with respect to the strong graph product. We finish by computing the Vietoris-Rips cohomology of the torus endowed with diferent semi-uniform structures.

arXiv comment12 pages, incorporated referee comments

References in corpus (4)

• The Vietoris-Rips complexes of a circle
• Cech Closure Spaces: A Unified Framework for Discrete and Continuous Homotopy
• Maximum likelihood estimation of regularisation parameters in high-dimensional inverse problems: an empirical Bayesian approach. Part II: Theoretical Analysis
• Vietoris-Rips Homology Theory for Semi-Uniform Spaces