A topological characterization of the Moufang property for compact polygons

TL;DR

This paper provides a topological characterization of the Moufang property for compact polygons, linking geometric properties to convergence groups, and explores automorphism groups of these structures.

Contribution

It introduces a new topological criterion for the Moufang property and extends understanding of automorphism groups in compact polygons without homogeneity assumptions.

Findings

Characterization of the Moufang property via convergence groups

A criterion for automorphism group compactness

Connection between automorphism groups and Bruhat-Tits buildings

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.