Property Testing and Expansion in Cubical Complexes

David Garber, Uzi Vishne

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)893-915
Number of pages23
JournalDiscrete and Computational Geometry
Issue number3
StatePublished - Apr 2021

Bibliographical note

Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.


  • Boolean functions
  • Cohomology of cubical complexes
  • Cubical complexes
  • Expansion
  • Incidence geometry
  • Property testing


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