Finite quotients of Bruhat-Tits buildings as geometric expanders

Abstract

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

14 pages

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