Isoperimetric Inequalities and topological overlapping for quotients of Affine buildings

TL;DR

This paper establishes isoperimetric inequalities for quotients of affine buildings and uses them to demonstrate topological overlapping properties of their 2-dimensional skeletons.

Contribution

It introduces new isoperimetric inequalities for affine building quotients and applies these to prove topological overlapping in their 2-skeletons.

Findings

Proved isoperimetric inequalities for affine building quotients.

Established topological overlapping for 2-dimensional skeletons.

Connected geometric inequalities to topological properties.

Abstract

We prove isoperimetric inequalities for quotients of $n$-dimensional Affine buildings. We use these inequalities to prove topological overlapping for the 2-dimensional skeletons of these buildings.