---
abstract: 'We prove a purely topological characterization of the Moufang property for disconnected compact polygons in terms of convergence groups. As a consequence, we recover the fact that a locally finite thick affine building of rank $3$ is a Bruhat–Tits building if and only if its automorphism group is strongly transitive. We also study automorphism groups of general compact polygons without any homogeneity assumption. A compactness criterion for sets of automorphisms is established, generalizing the theorem by Burns and Spatzier that the full automorphism group, endowed with the compact-open topology, is a locally compact group.'
author:
- 'Nicolas Radu[^1]'
date: 'July 15, 2016'
title: |
    A topological characterization of the Moufang\
    property for compact polygons
---

Introduction
============

Compact buildings form a natural generalization of compact projective planes. They were introduced by Burns and Spatzier in [@Burns], and used in their proof of the Rank Rigidity Theorem for Riemannian manifolds of non-positive sectional curvature, see [@Burns2]. A prominent example of a compact building is provided by the spherical building associated with a semisimple algebraic group over a non-discrete locally compact field. Since the origin, the problem of characterizing those buildings associated with semisimple algebraic groups among all compact buildings 