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Bounded-degree coboundary expanders
Constructs arbitrarily large finite d-dimensional simplicial complexes, for every d ≥ 3, with uniformly bounded vertex degrees and uniform 𝔽 coboundary expansion in every degree below d. Together with the known graph and two-dimensional cases, this establishes the existence of such expanders in every positive dimension.
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Bounded-degree coboundary expanders in every dimension
Sep 24, 2026·paper.pdf
For every integer d ≥ 3, we construct arbitrarily large finite d-dimensional simplicial complexes with uniformly bounded vertex degrees and uniform 𝔽 coboundary expansion in every degree below d. Together with the known graph and two-dimensional cases, this establishes the existence of bounded-degree 𝔽 coboundary expanders in every positive dimension.