Discrete & Computational Geometry | 2021
Property Testing and Expansion in Cubical Complexes
Abstract
We consider expansion and property testing in the language of incidence geometry, covering both simplicial and cubical complexes in any dimension. We develop a general method for the transition from an explicit description of the cohomology group, which need not be trivial, to a testability proof with linear ratio between errors. The method is demonstrated by testing functions on 2-cells in cubical complexes to be induced from the edges.