ECCC-Report TR19-126https://eccc.weizmann.ac.il/report/2019/126Comments and Revisions published for TR19-126en-usThu, 19 Sep 2019 22:04:54 +0300
Paper TR19-126
| Near Coverings and Cosystolic Expansion -- an example of topological property testing |
Irit Dinur,
Roy Meshulam
https://eccc.weizmann.ac.il/report/2019/126We 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 an example, we show that the 2-dimensional spherical building A3(????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.Thu, 19 Sep 2019 22:04:54 +0300https://eccc.weizmann.ac.il/report/2019/126