Bounded-degree coboundary expanders in every dimension
For every integer d ≥ 3, we construct arbitrarily large finite d -dimensional simplicial complexes with uniformly bounded vertex degrees and uniform 𝔽 2 coboundary expansion in every degree below d . Together with the known graph and two-dimensional cases, this establishes the existence of bounded-degree 𝔽 2 coboundary expanders in every positive dimension.
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Updates: Sharing AI progress on mathematics (amazing!); and my lecture plansCombinatorics and moreOct 7, 2026
The new construction gives arbitrarily large complexes in every dimension (d\ge3), with bounded vertex degrees and uniform (\mathbb F_2) coboundary expansion in every degree below (d). Amenability of Thompson’s group (F). My post The Thompson Group (2009) introduced the group of dyadic…