A topological characterization of the Moufang property for compact polygons

Radu, Nicolas

doi:10.1090/tran/6737

A topological characterization of the Moufang property for compact polygons
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Trans. Amer. Math. Soc. 369 (2017), 2151-2181 Request permission

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.

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