Property testing and expansion in cubical complexes

David Garber, Uzi Vishne

Published 2018-09-27Version 1

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 passing from an explicit description of the cohomology group, which need not be trivial, to a testability proof. The method is demonstrated by testing functions on $2$-cells in cubical complexes to be induced from the edges.