A topological characterization of the Moufang property for compact polygons

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.

30 pages, 10 figures

References in corpus (2)

• Trees, contraction groups, and Moufang sets
• Locally compact convergence groups and n-transitive actions

Cited by in corpus (1)

• A homogeneous ${\tilde{A}}_2$-building with a non-discrete automorphism group is Bruhat-Tits