Groups, Geometry, and Dynamics

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Volume 10, Issue 1, 2016, pp. 155–175
DOI: 10.4171/GGD/346

Published online: 2016-02-09

Expansion of building-like complexes

Alexander Lubotzky[1], Roy Meshulam[2] and Shahar Mozes[3]

(1) Hebrew University, Jerusalem, Israel
(2) Technion - Israel Institute of Technology, Haifa, Israel
(3) Hebrew University, Jerusalem, Israel

Following Gromov, the coboundary expansion of building-like complexes is studied. In particular, it is shown that for any $n \geq 1$, there exists a constant $\epsilon (n) > 0$ such that for any $0 \leq k < n$ the $k$-th coboundary expansion constant of any $n$-dimensional spherical building is at least $\epsilon (n)$.

Keywords: High dimensional expansion, spherical buildings

Lubotzky Alexander, Meshulam Roy, Mozes Shahar: Expansion of building-like complexes. Groups Geom. Dyn. 10 (2016), 155-175. doi: 10.4171/GGD/346