Near Coverings and Cosystolic Expansion – an example of topological property testing [article]

Irit Dinur, Roy Meshulam
2019 arXiv   pre-print
We study the stability of covers of simplicial complexes. Given a map f:Y→ X that satisfies almost all of the local conditions of being a cover, is it close to being a genuine cover of X? Complexes X for which this holds are called cover-stable. We show that this is equivalent to X being a cosystolic expander with respect to non-abelian coefficients. This gives a new combinatorial-topological interpretation to cosystolic expansion which is a well studied notion of high dimensional expansion. As
more » ... an example, we show that the 2-dimensional spherical building A_3(F_q) is cover-stable. We view this work as a possibly first example of "topological property testing", where one is interested in studying stability of a topological notion that is naturally defined by local conditions.
arXiv:1909.08507v1 fatcat:l4csd67gyndhnflnw2rc2miln4