Expansion of Building-Like Complexes

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