A topological characterization of the Moufang property for compact polygons

Radu, Nicolas
(2017) Transactions of the American mathematical society — Vol. 369, n° 3, p. 2151-2181 (2017)

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  • Radu, NicolasUCLouvain
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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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Radu, N. (2017). A topological characterization of the Moufang property for compact polygons. Transactions of the American mathematical society, 369(3), 2151-2181. https://doi.org/10.1090/tran/6737 (Original work published 2017)