Expansion of Building-Like Complexes

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 $ε(n)>0$ such that for any $0 \leq k <n$ the $k$-th coboundary expansion constant of any $n$-dimensional spherical building is at least $ε(n)$.

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