Compact Totally Disconnected Moufang Buildings
Theo Grundhofer, Linus Kramer, Hendrik Van Maldeghem, Richard M. Weiss

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 be a spherical building each of whose irreducible components is infinite, has rank at least 2 and satisfies the Moufang condition. We show that can be given the structure of a topological building that is compact and totally disconnected precisely when is the building at infinity of a locally finite affine building.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra
