Expansion of Building-Like Complexes

TL;DR

This paper proves that all n-dimensional spherical buildings have a uniform positive lower bound on their coboundary expansion constants across all dimensions less than n, extending Gromov's work.

Contribution

It establishes a uniform positive lower bound for the coboundary expansion constants of n-dimensional spherical buildings for all dimensions less than n.

Findings

Existence of a positive constant (n) for all n-dimensional spherical buildings

Uniform lower bounds on coboundary expansion constants across dimensions

Extension of Gromov's results to building-like complexes

Abstract

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 $\epsilon(n)$.