Near Coverings and Cosystolic Expansion -- an example of topological property testing
| Autor: | Dinur, Irit, Meshulam, Roy |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the stability of covers of simplicial complexes. Given a map $f:Y\to X$ 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 $A_{3}(\mathbb{F}_q)$ 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. Comment: 15 pages, 1 figure |
| Databáze: | arXiv |
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