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arXiv · 1503.08626

Finite quotients of Bruhat-Tits buildings as geometric expanders

Shai Evra
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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 $\tilde{A_d}$-buildings, for $d\geq 2$, over local fields. In this paper, this result is extended to general high rank Bruhat-Tits buildings.

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Shai Evra. 2015-11-05. Finite quotients of Bruhat-Tits buildings as geometric expanders. https://doi.org/10.1142/s1793525317500078

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