High dimensional expanders and property testing

Authors:
Tali Kaufman;Alexander Lubotzky
Affiliations:
BIU, Ramat Gan, Israel;Hebrew University, Jerusalem, Israel
Venue:
Proceedings of the 5th conference on Innovations in theoretical computer science
Year:
2014

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Abstract

We show that the high dimensional expansion property as defined by Gromov, Linial and Meshulam, for simplicial complexes is a form of testability. Namely, a simplicial complex is a high dimensional expander iff a suitable property is testable. Using this connection, we derive several testability results.