Coboundary expanders

By Dominic Dotterrer, Matthew Kahle. 2010

55 citations recorded by the source corpus.

We describe a higher-dimensional generalization of edge expansion for graphs which applies to arbitrary cell complexes. This generalization relies on a type of co-isoperimetric inequality. We utilize these inequalities to analyze the topological and geometric behavior of some families of random simplicial complexes.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/34d4d2514200de951c50571e40dfb1a42fe68398

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Random Walks on Simplicial Complexes and the normalized Hodge Laplacian (2018, background): “There are a number of connections between the spectra of matrices (such as the Hodge Laplacian) associated with SCs and notions of expansion [44,65,97,101,119].”
Spectral Gaps of Random Graphs and Applications (2012, background): “’s proof depends on “cohomological expansion,” a higher-dimensional analogue of edge expansion for graphs. This is closely related to the algebraic isoperimetry recently discussed by Gromov [22]. See [11] for a fuller discussion of these deﬁnitions in the context of random polyhedra, as well as [34]”
Sharp vanishing thresholds for cohomology of random flag complexes (2012, background): “the notion of expansion; see, for example, the discussion of random complexes as higher-dimensional expanders in [12].”