Finite quotients of Bruhat-Tits buildings as geometric expanders
Abstract
In FGLNP, Fox, Gromov, Lafforgue, Naor and Pach, in a respond to a question of Gromov G, constructed bounded degree geometric expanders, namely, simplical complexes having the affine overlapping property. Their explicit constructions are finite quotients of Ad-buildings, for d≥ 2, over local fields. In this paper, this result is extended to general high rank Bruhat-Tits buildings.
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