Compact Totally Disconnected Moufang Buildings

TL;DR

This paper characterizes when spherical Moufang buildings can be given a compact, totally disconnected topology, showing this occurs precisely for buildings at infinity of locally finite affine buildings.

Contribution

It provides a complete topological characterization of spherical Moufang buildings as boundaries of affine buildings.

Findings

Such buildings are compact and totally disconnected if and only if they are at infinity of a locally finite affine building.

The result links algebraic properties of buildings with their topological structure.

This characterization advances understanding of the structure of Moufang buildings in geometric group theory.

Abstract

Let $\Delta$ be a spherical building each of whose irreducible components is infinite, has rank at least 2 and satisfies the Moufang condition. We show that $\Delta$ can be given the structure of a topological building that is compact and totally disconnected precisely when $\Delta$ is the building at infinity of a locally finite affine building.