Expanders and right-angled Artin groups

The purpose of this paper is to give a characterization families expander graphs via right-angled Artin groups. We prove that sequence simplicial [Formula: see text] forms family if and only certain natural mini-max invariant arising from the cup product in cohomology rings groups agrees with Cheeger constant graphs, thus allowing us characterize cohomology. This result proved more general framework vector space expanders, novel structure consisting sequences spaces equipped vector-space-valued bilinear pairings which satisfy condition. These objects can be considered analogues realm linear algebra, dictionary being given by cohomology, context represent different approach expanders those developed Lubotzky–Zelmanov Bourgain–Yehudayoff.