Kunneth Theorems for Vietoris-Rips Homology
Antonio Rieser, Alejandra Trujillo
TL;DR
This paper establishes a Kunneth theorem for Vietoris-Rips homology and cohomology in semi-uniform spaces, applies it to graphs with strong product, and computes cohomology for the torus under various structures.
Contribution
It introduces a Kunneth theorem for Vietoris-Rips homology in semi-uniform spaces and extends it to graph products, providing new computational insights.
Findings
Kunneth theorem proven for semi-uniform spaces
Kunneth theorem shown for graphs with strong product
Vietoris-Rips cohomology computed for the torus
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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis · Geometric and Algebraic Topology